Recent zbMATH articles in MSC 74Fhttps://zbmath.org/atom/cc/74F2022-07-25T18:03:43.254055ZWerkzeugGeneral decay of Bresse system by modified thermoelasticity of type IIIhttps://zbmath.org/1487.350582022-07-25T18:03:43.254055Z"Dridi, Hanni"https://zbmath.org/authors/?q=ai:dridi.hanni"Saci, Marwa"https://zbmath.org/authors/?q=ai:saci.marwa"Djebabla, Abdelhak"https://zbmath.org/authors/?q=ai:djebabla.abdelhakSummary: In this paper we have studied the model for arched beams problem
\[
\begin{aligned}
&\rho_1\varphi_{tt}-k(\varphi_x+\psi +l\omega)_x-k_0l(\omega_x-l\varphi)=0,\\
&\rho_2\psi_{tt}-b\psi_{xx}+k(\varphi_x+\psi +l\omega)+\gamma \theta_{tx}=0,\\
&\rho_1\omega_{tt}-k_0(\omega_x-l\varphi)_x+kl(\varphi_x +\psi +l\omega)=0,\\
&\rho_3\theta_{tt}-\kappa \theta_{xx}+\beta (g*\theta_{xx})+\gamma \psi_{tx}=0,
\end{aligned}
\] which reduces to the classical Timoshenko system when the arch curvature \(l=0\), the asymptotic stability of one-dimensional Timoshenko system by thermoelasticity of type III was proved by \textit{A. Djebabla} and \textit{N. Tatar} [J. Dyn. Control Syst. 16, No. 2, 189--210 (2010; Zbl 1203.93173)]. The subject of this paper is to supplement these previous results by proving that the Bresse system which is considered a generalization of the Timoshenko system, is also subjected to the same sufficient condition that controls the stability of the Timoshenko system and we have shown that (exponential / polynomial) energy stability is achieved in an (exponential and polynomial) kernel function state.Exponential and polynomial stability results for networks of elastic and thermo-elastic rodshttps://zbmath.org/1487.350802022-07-25T18:03:43.254055Z"Hayek, Alaa"https://zbmath.org/authors/?q=ai:hayek.alaa"Nicaise, Serge"https://zbmath.org/authors/?q=ai:nicaise.serge"Salloum, Zaynab"https://zbmath.org/authors/?q=ai:salloum.zaynab"Wehbe, Ali"https://zbmath.org/authors/?q=ai:wehbe.aliSummary: In this paper, we investigate a network of elastic and thermo-elastic materials. On each thermo-elastic edge, we consider two coupled wave equations such that one of them is damped via a coupling with a heat equation. On each elastic edge (undamped), we consider two coupled conservative wave equations. Under some conditions, we prove that the thermal damping is enough to stabilize the whole system. If the two waves propagate with the same speed on each thermo-elastic edge, we show that the energy of the system decays exponentially. Otherwise, a polynomial energy decay is attained. Finally, we present some other boundary conditions and show that under sufficient conditions on the lengths of some elastic edges, the energy of the system decays exponentially on some particular networks similar to the ones considered in [\textit{F. Shel}, Math. Methods Appl. Sci. 36, No. 8, 869--879 (2013; Zbl 1267.35241)].Rigorous derivation of a linear sixth-order thin-film equation as a reduced model for thin fluid-thin structure interaction problemshttps://zbmath.org/1487.353142022-07-25T18:03:43.254055Z"Bukal, Mario"https://zbmath.org/authors/?q=ai:bukal.mario"Muha, Boris"https://zbmath.org/authors/?q=ai:muha.borisSummary: We analyze a linear 3D/3D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic plate-like structure with the aim of deriving a simplified reduced model. Based on suitable energy dissipation inequalities quantified in terms of two small parameters, thickness of the fluid layer and thickness of the elastic structure, we identify the right relation between the system coefficients and small parameters which eventually provide a reduced model on the vanishing limit. The reduced model is a linear sixth-order thin-film equation describing the out-of-plane displacement of the structure, which is justified in terms of weak convergence results relating its solution to the solutions of the original fluid-structure interaction problem. Furthermore, approximate solutions to the fluid-structure interaction problem are reconstructed from the reduced model and quantitative error estimates are obtained, which provide even strong convergence results.Thermal flows in fractured porous mediahttps://zbmath.org/1487.353172022-07-25T18:03:43.254055Z"Gruais, Isabelle"https://zbmath.org/authors/?q=ai:gruais.isabelle"Poliševski, Dan"https://zbmath.org/authors/?q=ai:polisevski.dan-aSummary: We consider the thermal flow problem occuring in a fractured porous medium. The incompressible filtration flow in the porous matrix and the viscous flow in the fractures obey the Boussinesq approximation of Darcy-Forchheimer law and respectively, the Stokes system. They are coupled by the Saffman's variant of the Beavers-Joseph condition. Existence and uniqueness properties are presented. The use of the energy norm in describing the Darcy-Forchheimer law proves to be appropriate. In the \(\varepsilon\)-periodic framework, we find the two-scale homogenized system which governs their asymptotic behaviours when \(\varepsilon \rightarrow 0\) and the Forchheimer effect vanishes. The limit problem is mainly a model of two coupled thermal flows, neither of them being incompressible.Study of the dielectric gradient values of reinforced concrete sample by considering radar measurements in an inverse problemhttps://zbmath.org/1487.353572022-07-25T18:03:43.254055Z"Ferrieres, X."https://zbmath.org/authors/?q=ai:ferrieres.xavier"Klysz, G."https://zbmath.org/authors/?q=ai:klysz.g"Guihard, V."https://zbmath.org/authors/?q=ai:guihard.vincent"Albrand, M."https://zbmath.org/authors/?q=ai:albrand.mSummary: The goal of this study is to develop a tool that will evaluate the moisture content gradient in the depth of reinforced concretes in the context of building safety. The monitoring of ageing phenomena, such as the corrosion of steel reinforcements, depends on the amount of water and on its gradient as they are directly related to the dielectric values of the concrete. In this paper, to obtain these values, we propose to solve an inverse problem for reinforced concrete. First, an experimental device based on radar measurements is proposed with its 3D numerical model. Next, we describe an inverse process to determine a dielectric profile according to the depth and validate it on measured data obtained for control samples.Unique identification of a multi-layered fluid-solid mediumhttps://zbmath.org/1487.354412022-07-25T18:03:43.254055Z"Cui, Yanli"https://zbmath.org/authors/?q=ai:cui.yanli"Li, Xiliang"https://zbmath.org/authors/?q=ai:li.xiliang"Qu, Fenglong"https://zbmath.org/authors/?q=ai:qu.fenglongSummary: This paper is concerned with the inverse scattering of time-harmonic acoustic plane waves by a multi-layered fluid-solid medium in the three dimensional space. We establish the global uniqueness in identifying the embedded penetrable solid obstacle, the surrounding fluid medium and its wave number from the acoustic far-field pattern for all incident plane waves at a fixed frequency. The proof depends on constructing different kinds of interior transmission problems in appropriate small domains and the a priori estimates derived for both the elastic wave fields in the embedded solid obstacle and the acoustic wave fields in the surrounding fluid medium.Spectral analysis of integro-differential equations arising in thermal physicshttps://zbmath.org/1487.450132022-07-25T18:03:43.254055Z"Pankratova, E. V."https://zbmath.org/authors/?q=ai:pankratova.ekaterina-v|pankratova.evgeniya-vThis paper is devoted to the spectrum of an operator function arising in the study of the following abstract second-order integro-differential equation in a separable Hilbert space \(H\):
\[
\frac{d^2u(t)}{dt^2} + \int \limits ^t_0 Q(t - s)\frac{du(s)}{ds} ds + A^2u(t) - \int \limits ^t_0 K(t - s)A^2 2u(s) ds = f(t), \tag{1}
\]
with \(t \in \mathbb{R}_+\) and initial conditions \(u(+0) = \varphi_0\), \(u^{\prime}(+0) = \varphi_1\). Here, \(A \) is a linear operator on \( H\) and \(A: \operatorname{Dom}(A) \to H\) is a self-adjoint positive definite operator with compact inverse.
The author is mainly interested in the spectral analysis of the operator function resulting from applying the Laplace transform to the left-hand side of Equation~(1). In particular, the localization of the spectrum of this operator function is obtained. The asymptotics of the non-real part of the spectrum is constructed.
Reviewer: Anar Assanova (Almaty)Strong dissipative hydrodynamical systems and the operator pencil of S. Kreinhttps://zbmath.org/1487.470262022-07-25T18:03:43.254055Z"Voytitsky, V. I."https://zbmath.org/authors/?q=ai:voytitsky.victor-ivanovichThis review article is devoted to the linear operator differential equation \(u''(t)+(A+iG)u'(t)+Bu(t)=f(t)\) provided strong dissipativeness and to spectral properties of the related operator pencil of the form \(L(\lambda)=I-\lambda S-\lambda^{-1}T\) in a Hilbert space. The paper deals with factorization problems and asymptotics for eigenvalues of the pencil. Such type of equations and pencils arise in hydrodynamics. The author considers applications to the following problems:
\begin{itemize}
\item normal oscillations of viscous liquid in an open vessel,
\item normal oscillations of heavy rotating liquid in an open vessel,
\item normal convective movements of heavy liquid in an open vessel,
\item normal oscillations of joined pendulums with cavities filled with viscous liquids.
\end{itemize}
Reviewer: Nikita V. Artamonov (Moskva)Numerical analysis of a porous-elastic model for convection enhanced drug deliveryhttps://zbmath.org/1487.651482022-07-25T18:03:43.254055Z"Ferreira, J. A."https://zbmath.org/authors/?q=ai:ferreira.jose-augusto"Pinto, L."https://zbmath.org/authors/?q=ai:pinto.linu"Santos, R. F."https://zbmath.org/authors/?q=ai:santos.rita-filomena|santos.rui-filipe|santos.rafael-fThe authors of this work studied a coupled system of partial differential equations stemming from modeling of the technique of convection-enhanced drug delivery in an elastic medium. The main contribution of the work is the numerical analysis of a piecewise linear finite element method used for the numerical solution of the system. The authors derived energy and stability estimates for the continuous and discrete pressure, displacement, and concentration variables, and conducted a convergence analysis. Second-order convergence for the three discrete quantities in suitable norms was proven. These estimates were verified by a one-dimensional numerical example. Additional one-dimensional numerical examples with varying elastic properties of tissues were presented.
Reviewer: Baasansuren Jadamba (Rochester)On the description of deceleration of a body in a medium flowhttps://zbmath.org/1487.700302022-07-25T18:03:43.254055Z"Samsonov, V. A."https://zbmath.org/authors/?q=ai:samsonov.vitaly-a"Selyutskiĭ, Yu. D."https://zbmath.org/authors/?q=ai:selyutskii.yu-d(no abstract)Bulk and surface acoustic waves. Fundamentals, devices, and applicationshttps://zbmath.org/1487.740042022-07-25T18:03:43.254055Z"Zhang, Guigen"https://zbmath.org/authors/?q=ai:zhang.guigenPublisher's description: This book introduces acoustic wave theories using a reader-friendly matrix-based linear algebra approach. It will enable the reader to take advantage of software tools such as MATLAB (commercial codes) and OCTAVE (open-source codes) to gain better and deeper understanding of the underlying physics quickly. In this aspect, this text can be regarded as a practical introduction of the acoustic wave theories in an easy-to-follow linear algebra format using matrix manipulations instead of an abstract approach relying on tensor manipulations. The book also uses case studies to demonstrate how the fundamentals on acoustic waves discussed throughout the book are applied in device designs and analyses such that the connections and interdependences between the underlying sciences and the observed behavior and performances can be better appreciated by the reader. To achieve this, all problems for illustrations, examples, case studies, and device analyses are developed and solved based on the mathematical foundations laid out in the book.Modeling the temperature, crystallization, and residual stress for selective laser sintering of polymeric powderhttps://zbmath.org/1487.740212022-07-25T18:03:43.254055Z"Shen, Fei"https://zbmath.org/authors/?q=ai:shen.fei"Zhu, Wei"https://zbmath.org/authors/?q=ai:zhu.wei"Zhou, Kun"https://zbmath.org/authors/?q=ai:zhou.kun"Ke, Liao-Liang"https://zbmath.org/authors/?q=ai:ke.liaoliangSummary: A thermomechanical model is developed to predict the temperature, degree of crystallization, residual stress, and strain in the selective laser sintering process for polymeric powder. Especially, a transient heat transfer model is used to calculate the temperature evolution. An elastic-viscoplastic model is developed to describe the temperature- and time-dependent stress-strain behavior of polymeric materials with crystallization-induced strain being included. A crystallization model is used to predict the relative crystallization degree during the cooling process. The sintering process and cooling process of polyamide 12 are simulated using the developed model. The melt pool depth and the deformation of the printed parts are validated by the experimental results. The evolutions of the temperature, relative degree of crystallization, strain, and stress are evaluated. The effects of the cooling rate on the strain and stress evolutions are discussed.Transient thermoelastic problem in a confocal elliptical disc with internal heat sourceshttps://zbmath.org/1487.740242022-07-25T18:03:43.254055Z"Bhad, Pravin P."https://zbmath.org/authors/?q=ai:bhad.pravin-p"Khalsa, Lalsingh H."https://zbmath.org/authors/?q=ai:khalsa.lalsingh-h"Varghese, Vinod"https://zbmath.org/authors/?q=ai:varghese.vinodSummary: An exact solution is found for the thermoelastic responses in an elliptical disc due to interior heat generation within the solid, under thermal boundary conditions that are subjected to arbitrary initial temperature on the upper and lower face at zero temperature, with radiation boundary conditions on both surfaces. The method of integral transformation technique is used to generate an exact solution of heat conduction equation in which sources are generated according to the linear function of the temperature. The determination of displacement and stresses was performed by means of Airy's stress function approach. The numerical results obtained using these computational tools are accurate enough for practical purposes.Basic problems of thermoelasticity with microtemperatures for the circlehttps://zbmath.org/1487.740252022-07-25T18:03:43.254055Z"Bitsadze, L."https://zbmath.org/authors/?q=ai:bitsadze.lamara|bitsadze.l-pSummary: The present paper is devoted to the explicit solution of the Dirichlet type BVP for an elastic circle with microtemperatures. The regular solution of the system of equations for an isotropic materials with microtemperatures is constructed by means of the elementary (harmonic, bi-harmonic and meta-harmonic) functions. The Dirichlet type BVP for a circle is solved explicitly. The obtained solutions are presented as absolutely and uniformly convergent series.Some BVP in the plane theory of thermodynamics with microtemperatureshttps://zbmath.org/1487.740262022-07-25T18:03:43.254055Z"Gulua, B."https://zbmath.org/authors/?q=ai:gulua.bakur"Janjgava, R."https://zbmath.org/authors/?q=ai:janjgava.roman"Kasrashvili, T."https://zbmath.org/authors/?q=ai:kasrashvili.tamar"Narmania, M."https://zbmath.org/authors/?q=ai:narmania.mirandaSummary: In this work we consider the two-dimensional version of statics of the linear theory of elastic materials with inner structure whose particles, in addition to the classical displacement and temperature fields, possess microtemperatures. The Dirichlet BVP is solved for a circle.Irreversible deformation under thermomechanical loading of solidshttps://zbmath.org/1487.740272022-07-25T18:03:43.254055Z"Kikvidze, O. G."https://zbmath.org/authors/?q=ai:kikvidze.o-gSummary: The article considers irreversible deformation of solid under thermomechanical loading, using the phenomenological approach. It is assumed that the strains are small. On the basis of the dilatometric curves and the stress-strain curves, the condition was formulated for the stability of material, and the major inequality and constitutive equations for the irreversible strains under thermo-mechanical loading were obtained. These equations describe the pattern of inelastic deformation of a wide class of metallic materials in the temperature ranges of the phase transformations.Galerkin-type solution for the Moore-Gibson-Thompson thermoelasticity theoryhttps://zbmath.org/1487.740282022-07-25T18:03:43.254055Z"Singh, Bhagwan"https://zbmath.org/authors/?q=ai:singh.bhagwan"Mukhopadhyay, Santwana"https://zbmath.org/authors/?q=ai:mukhopadhyay.santwanaSummary: It is prominent that the Galerkin-type representation plays a dominant role in probing various challenges of mathematical physics, continuum mechanics and occupies an important place in the field of partial differential equations (PDEs). Thus, the contemporary analysis of different boundary value problems (BVPs) in thermoelasticity theory commonly begins by analyzing the Galerkin-type representation of the field equations in terms of elementary functions (harmonic, biharmonic, and metaharmonic, etc). This work is aimed at formulating the representation of a Galerkin-type solution by means of elementary functions for the recently developed Moore-Gibson-Thompson (MGT) thermoelasticity theory. The MGT theory is a generalized form of the Lord-Shulman (LS) model as well as of the Green-Naghdi (GN) thermoelastic model. Here, we establish a theorem and derive the Galerkin-type solution for the basic governing equations under this theory. Later, the Galerkin representation of a system of equations for steady oscillations is derived. Based on this representation, we finally establish the general solution (GS) for the system of homogeneous equations of stable oscillation, neglecting the extrinsic body force and extrinsic heat supply.Modeling of memory dependent derivative under three-phase lag in generalized thermo-viscoelasticityhttps://zbmath.org/1487.740292022-07-25T18:03:43.254055Z"Singh, Biswajit"https://zbmath.org/authors/?q=ai:singh.biswajit"Sarkar, Smita Pal"https://zbmath.org/authors/?q=ai:pal-sarkar.smita"Barman, Krishnendu"https://zbmath.org/authors/?q=ai:barman.krishnenduSummary: In this study, a new generalized model of thermo-viscoelasticity with three phase-lag (TPL) theory concerning memory-dependent derivative (MDD) theory is emphasized. The governing combined equations of the novel model associated with kernel function and time delay are considered in a two-dimensional semi-infinite space. The bounding surface of the medium is assumed to be free of traction and subjected to time-dependent thermal loading. Using Laplace and Fourier Transform techniques, the problem is transformed from the space-time domain and then solved numerically. Suitable numerical technique is used to find the inversion of Fourier and Laplace transforms. In the simulation, the effects of the time-delay parameter and kernel function on the distributions of the displacement components, stresses and temperature field are studied and represented graphically. The results shows that the presence of TPL, the time-delay and kernel function extensively affect all the distributions.Transient-thermoelastic analysis of periodically rotated functionally graded hollow cylinderhttps://zbmath.org/1487.740302022-07-25T18:03:43.254055Z"Yarımpabuç, Durmuş"https://zbmath.org/authors/?q=ai:yarimpabuc.durmusSummary: A closed-form solution for transient thermal stress analysis of functionally graded hollow cylinder exposed to high-temperature difference is obtained under the influence of periodic rotation. All mechanical and thermal properties except the Poisson's ratio are assumed to be graded in the radial direction as a power-law function. The transient heat conduction and equilibrium equations are solved on the Laplace domain by using Bessel functions and the Gauss quadrature integration procedure. The inverse transformation to the real space is achieved by using the modified Durbin method. The novelty of this study is to provide a general solution to the functionally graded cylinder under the effect of periodic rotation in a transient regime. The effects of periodic rotation and high-temperature difference on temperature and thermal stresses are investigated for a specific ceramic-metal mixture by using this solution. The solution presented in this study can be adopted simply by changing the coefficients of inhomogeneity in the power-law variation for any pair of materials.An introduction to quasi-static aeroelasticityhttps://zbmath.org/1487.740312022-07-25T18:03:43.254055Z"Destuynder, Philippe"https://zbmath.org/authors/?q=ai:destuynder.philippe"Fabre, Caroline"https://zbmath.org/authors/?q=ai:fabre.carolineSummary: The aeroelasticity is the science which models, analyses and describes the coupled movements between a flow and a flexible structure. The different phenomena encountered can be classified using three (at least) adimensional numbers: the Strouhal number, the Reynolds number and the reduce frequency number (which despite its name, has no dimension). For sake of clarity, let us just mention in this abstract, that the reduce frequency is the ratio between the time necessary to a flow particle for flying over a flexible structure and the fundamental period of oscillation of this structure.
In the framework of quasi-static aeroelasticity, it is always assumed that the reduce frequency is smaller than the unity. It enables one to define the flow fields (velocity, pressure) from a static position of the structure. The effect of its position with respect to the flow leads to a modification of the stiffness (added aerodynamic stiffness). Furthermore, the relative flow velocity (difference between the flow velocity and the one of the structure) leads to introduce damping due to the flow and therefore modifies the static analysis of stability into the dynamic stability study (aerodynamic damping).
Recently, engineers have upgraded this approach by introducing the added mass concept. This is a mechanical effect due to the fact that the inertia of the structure should take into account the mass of flow which is involved in a movement. This is performed using an incompressible and inviscid model which gives a retroaction effect on the structure proportionally to its velocity. The two first parts of this text are devoted to a formulation of this three effects which are necessary in the dynamic modeling of a flexible (or not) structure immersed in a flow (air or water for instance). Examples in civil engineering and aerodynamics are given in order to illustrate the theoretical formulation. Few control aspects in a dynamic behavior of the coupled fluid-structure modeling are also discussed in a section of this text.
For the entire collection see [Zbl 1471.65004].A closed-form yield criterion for porous materials with Mises-Schleicher-Burzyński matrix containing cylindrical voidshttps://zbmath.org/1487.740322022-07-25T18:03:43.254055Z"dos Santos, Tiago"https://zbmath.org/authors/?q=ai:dos-santos.tiago"Vadillo, Guadalupe"https://zbmath.org/authors/?q=ai:vadillo.guadalupeSummary: This work develops a closed-form yield criterion applicable to porous materials with pressure-dependent matrix presenting tension-compression asymmetry (Mises-Schleicher-Burzyński material) containing parallel cylindrical voids. To develop the strength criterion, the stress-based variational homogenization approach due to [\textit{L. Cheng} et al., ``A stress-based variational model for ductile porous materials'', Int J. Plast. 55, 133--151 (2014; \url{doi:10.1016/j.ijplas.2013.10.003})] is extended to the case of a hollow cylinder under generalized plane strain conditions subjected to axisymmetric loading. Adopting a strictly statically admissible trial stress field, the homogenization procedure results in an approximate yield locus depending on the current material porosity, tension-compression material asymmetry, the mean lateral stress, and an equivalent shear stress. The analytical criterion provides exact solutions for purely hydrostatic loading. Theoretical results are compared with finite element (FE) simulations considering cylindrical unit-cells with distinct porosity levels, different values of the tension-compression asymmetry, and a wide range of stress triaxialities. Based on comparisons, the theoretical results are found to be in good agreement with FE simulations for most of the loading conditions and material features considered in this study. More accurate theoretical predictions are provided when higher material porosities and/or lower tension-compression asymmetries are considered. Overall, the main outcome of this work is a closed-form yield function proving fairly accurate predictions to engineering applications, in which pressure-dependent and tension-compression asymmetric porous materials with cylindrical voids are dealt with. This can be the case of honeycomb structures or additively manufactured materials, in which metal matrix composites are employed.Finite strain modelling for multiphase flow in dual scale porous media during resin infusion processhttps://zbmath.org/1487.740332022-07-25T18:03:43.254055Z"Huang, Ruoyu"https://zbmath.org/authors/?q=ai:huang.ruoyuSummary: Resin infusion is a pressure-gradient-driven composite manufacturing process in which the liquid resin is driven to flow through and fill in the void space of a porous composite preform prior to the heat treatment for resin solidification. It usually is a great challenge to design both the infusion system and the infusion process meeting the manufacturing requirements, especially for large-scale components of aircraft and wind turbine blades. Aiming at addressing the key concerns about flow fronts and air bubble entrapment, the present study proposes a modelling framework of the multiphase flow of resin and air in a dual scale porous medium, i.e. a composite preform. A finite strain formulation is discussed for the fluid-solid interaction during an infusion process. The present study bridges the gap between the microscopic observation and the macroscopic modelling by using the averaging method and first principle method, which sheds new light on the high-fidelity finite element modelling.A simplified model for hydroelasticity of containershipshttps://zbmath.org/1487.740342022-07-25T18:03:43.254055Z"Sengupta, Debasmit"https://zbmath.org/authors/?q=ai:sengupta.debasmit"Datta, Ranadev"https://zbmath.org/authors/?q=ai:datta.ranadev"Sen, Debabrata"https://zbmath.org/authors/?q=ai:sen.debabrataSummary: In this work, a semi-analytic method has been developed to perform the hydroelasticity analysis of containerships. For the solution of the hydrodynamic problem, a time-domain method is developed based on impulse response function (IRF); however, for the solution of the structural responses, modal superposition technique is used assuming the ship is based on Euler-Bernoulli beam theory. The time-domain amplitude of the displacements and velocities corresponding to several modes is then determined using a semi-analytic approach using Duhamel integral technique. In this paper, the effect of structural flexibility in the calculation of structural displacement, shear force, and bending moment is studied. To check the efficiency and correctness of the proposed semi-analytic method, initially, the computed results are compared with published and experimental results for two container ships with different lengths. In the second phase, a comparative study has been made to check the effect of several physical and geometric parameters such as ship length, vessel speed, and wavelength to ship length ratio. It is seen from the comparative study that ship length, Froude number, wave to ship length ratio, etc. have a significant effect in the calculations of global bending moment, shear force. From the computed results, it may be concluded that the proposed semi-analytic approach is capable of generating results within an acceptable range of engineering accuracy with negligible computational effort, and thus, it can be a very useful tool for preliminary design load for larger vessels.Potential method in the coupled theory of elastic double-porosity materialshttps://zbmath.org/1487.740352022-07-25T18:03:43.254055Z"Svanadze, Merab"https://zbmath.org/authors/?q=ai:svanadze.merab-zhSummary: In the present paper the linear coupled model of elastic double-porosity materials is proposed in which the coupled phenomenon of the concepts of Darcy's law and the volume fraction is considered. The basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Indeed, the fundamental solution of the system of steady vibration equations is constructed explicitly by means of elementary functions, and its basic properties are presented. The radiation conditions are established, and Green's identities are obtained. The uniqueness theorems for the regular (classical) solutions of the BVPs are proved. The surface (single-layer and double-layer) and volume potentials are constructed, and the basic properties of these potentials are given. The determinants of symbolic matrices of the singular integral operators are calculated explicitly. Then, the BVPs are reduced to the always solvable singular integral equations for which Fredholm's theorems are valid. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.Mathematical model for a magneto-thermoelastic micropolar medium with temperature-dependent material moduli under the effect of mechanical strip loadhttps://zbmath.org/1487.740362022-07-25T18:03:43.254055Z"Alharbi, Amnah M."https://zbmath.org/authors/?q=ai:alharbi.amnah-m"Said, Samia M."https://zbmath.org/authors/?q=ai:said.samia-m"Abd-Elaziz, Elsayed M."https://zbmath.org/authors/?q=ai:abd-elaziz.elsayed-m"Othman, Mohamed I. A."https://zbmath.org/authors/?q=ai:othman.mohamed-ibrahim-ahmedSummary: A new model of equations of generalized thermoelasticity for an isotropic medium with mechanical properties that are dependent on temperature is established. The present problem is a generalization of the three-phase-lag model, Lord and Shulman's coupled theory. The elasticity modulus is a reference temperature function which is linear. Analytical expressions of the considered variables are obtained by using the Laplace-Fourier transforms technique. The results are analysed in a deeper manner by comparing them with unique cases of absence of the magnetic field, temperature-dependent properties of the body, and two types of mechanical loads. The most significant points are highlighted.On the effect of the volumetric deformation in soft dielectric composites with high phase contrasthttps://zbmath.org/1487.740372022-07-25T18:03:43.254055Z"Bardella, Lorenzo"https://zbmath.org/authors/?q=ai:bardella.lorenzo"Volpini, Valentina"https://zbmath.org/authors/?q=ai:volpini.valentina"Gei, Massimiliano"https://zbmath.org/authors/?q=ai:gei.massimilianoSummary: Towards the accurate modelling of soft dielectric composites, this investigation aims at demonstrating that the incompressibility constraint customarily adopted in the literature may lead to largely inaccurate predictions. This claim is grounded on the premise that, even though in these composites each phase may individually be assumed to be incompressible, the volumetric deformation of the softest phase can provide a significant contribution to the effective behaviour if the phase contrast is high enough. To reach our goal, we determine the actuation response of two-phase dielectric laminated composites (DLCs) where the softest phase admits volumetric deformation. Our results, discussed in the light of the limit case in which the softest phase consists of vacuum, on the one hand, challenge the hypotheses usually assumed in the modelling of soft dielectric composites and, on the other hand, are expected to provide useful information for the design of high-performance hierarchical DLCs.Modeling of electro-viscoelastic dielectric elastomer: a continuum mechanics approachhttps://zbmath.org/1487.740382022-07-25T18:03:43.254055Z"Behera, Subrat Kumar"https://zbmath.org/authors/?q=ai:behera.subrat-kumar"Kumar, Deepak"https://zbmath.org/authors/?q=ai:kumar.deepak"Sarangi, Somnath"https://zbmath.org/authors/?q=ai:sarangi.somnathThe authors derive a micro-mechanics-based rheological model for an incompressible isotropic electro-viscoelastic material. Such electroactive polymers may develop large strains under electrical loads.
The proposed model needs only three material parameters: shear modulus, minimal extensibility and viscosity coefficient to fit the available experimental data. This is half the number of material parameters introduced in earlier work.
In deriving the constitutive theory, the authors use a multiplicative deformation gradient decomposition into elastic and viscous parts. The derived constitutive relations are thermodynamically admissible. In developing their theory, the authors assume that the electric field equilibrates faster than the deformation, thus implying that the electric field does not affect the dissipation.
The proposed model is validated using results from uniaxial experimental data, and good agreement is reached.
Some conclusions are discussed concerning the ability of the model to describe the rheological behavior of dielectric elastomers.
Reviewer: Ahmed Ghaleb (Giza)Stress effects on electric currents in antiplane problems of piezoelectric semiconductors over a rectangular domainhttps://zbmath.org/1487.740392022-07-25T18:03:43.254055Z"He, Jialei"https://zbmath.org/authors/?q=ai:he.jialei"Du, Jianke"https://zbmath.org/authors/?q=ai:du.jianke"Yang, Jiashi"https://zbmath.org/authors/?q=ai:yang.jiashiSummary: We study stress-induced electric potential and mobile charge distributions in antiplane deformations of piezoelectric semiconductors. The macroscopic theory of piezoelectric semiconductors is used. A double trigonometric series solution is obtained for the linearized problem over a rectangular domain, showing the formation of electric potential barriers or wells under local mechanical loads. A nonlinear numerical analysis is performed using COMSOL to obtain the current-voltage relation and the current density distribution. Results show that the stress-induced potential barriers/wells affect the electric current distributions and current-voltage relation. Thus, mechanical loads affect the semiconduction in the body, which is the foundation of piezotronic devices made from piezoelectric semiconductors. The effects of various physical and geometric parameters are examined.Seebeck effect on magneto-thermo-viscoelastic homogeneous isotropic hollow cylinder with Green-Naghdi theoryhttps://zbmath.org/1487.740402022-07-25T18:03:43.254055Z"Khamis, A. K."https://zbmath.org/authors/?q=ai:khamis.alaa-k"Nasr, Amir Mohamed Abdel Allah"https://zbmath.org/authors/?q=ai:nasr.amir-mohamed-abdel-allah"El-Bary, A. A."https://zbmath.org/authors/?q=ai:el-bary.alaa-a|el-bary.alla-a"Atef, Haitham M."https://zbmath.org/authors/?q=ai:atef.haitham-mThe authors consider a boundary value problem of magneto-thermo-viscoelasticity for an infinite cylinder of an isotropic, perfect electrical conductor, within the frame of extended thermodynamics under Green and Naghdi hypothesis of zero dissipation. Ohm's law for electric conduction is generalized to include the thermal gradient (Seebeck effect).
The body is subjected to an initially constant magnetic field along the angular coordinate of a cylindrical system of coordinates with z-axis coinciding with the axis of the cylinder. The external boundary is stress-free and subjected to a constant thermal shock.
Symmetry considerations allow for a solution depending only on the radial coordinate and time. The problem is solved by the Laplace transform technique with numerical inversion based on Fourier expansion. Application of the boundary conditions is not shown in the text.
The results for radial displacement, strain and normal stress are plotted as functions of time or distance, for different values of material parameters and initial magnetic field.
Reviewer: Ahmed Ghaleb (Giza)Green's functions for a trigonal piezoelectric half-plane belonging to 3m crystal classhttps://zbmath.org/1487.740412022-07-25T18:03:43.254055Z"Kharrazi, Hossein"https://zbmath.org/authors/?q=ai:kharrazi.hossein"Khojasteh, Ali"https://zbmath.org/authors/?q=ai:khojasteh.ali"Rahimian, Mohammad"https://zbmath.org/authors/?q=ai:rahimian.mohammad-hassan|rahimian.mohammad-amin"Pak, Ronald Y. S."https://zbmath.org/authors/?q=ai:pak.ronald-y-sSummary: Piezoelectric materials have a wide range of industrial applications in different branches of engineering due to their electromechanical coupling. So, investigating their responses to either mechanical or electric loadings helps engineers for efficient design of smart systems. However, most of the studies have assessed the well-known 6 mm piezoelectric materials or piezoceramics and few papers have studied other piezoelectric crystals despite of their application in industry. In this paper, fundamental solutions of a trigonal piezoelectric half-plane belonging to 3m crystal class is obtained. The governing differential equations are derived and solved analytically using potential method. It is shown that the solution for the 3m material can be degenerated to 6 mm solution as a special case. The contour lines were depicted for two practical piezoelectric materials belonging to 3m and 6 mm crystal classes including lithium niobate and PZT-4 and they were compared to each other. The numerical results showed that the response of the trigonal material is asymmetric due to anisotropy and the effect of anisotropy on some responses is considerable causing totally different behavior from 6 mm piezoelectric material.Simulation of antiplane piezoelectricity problems with multiple inclusions using the generalized finite difference methodhttps://zbmath.org/1487.740422022-07-25T18:03:43.254055Z"Yu, Hao"https://zbmath.org/authors/?q=ai:yu.hao.2|yu.hao.4|yu.hao|yu.hao.3|yu.hao.1"Lin, Ji"https://zbmath.org/authors/?q=ai:lin.jiSummary: In this paper, antiplane piezoelectricity problems with multiple inclusions are studied by the generalized finite difference method (GFDM). Developed from the Taylor series and the Moving Least Squares, the GFDM expresses the derivatives of variables as the combination of values of surrounding nodes where the sparse matrix will be obtained considering the boundary conditions and interface conditions. Stress concentration and electric field concentration are analyzed in three numerical examples, which contain circular and elliptical piezoelectric inclusions in various sizes, locations, and material parameters. The applicability and validity of the proposed method are verified through the comparison with reference results.Vibration isolation and energy harvesting integrated in a Stewart platform with high static and low dynamic stiffnesshttps://zbmath.org/1487.740522022-07-25T18:03:43.254055Z"Lu, Ze-Qi"https://zbmath.org/authors/?q=ai:lu.zeqi"Wu, Dao"https://zbmath.org/authors/?q=ai:wu.dao"Ding, Hu"https://zbmath.org/authors/?q=ai:ding.hu"Chen, Li-Qun"https://zbmath.org/authors/?q=ai:chen.liqunSummary: An electromagnetic Stewart platform with high static and low dynamic stiffness is explored to reduce the vibration in six degrees of freedom (6-dofs) and simultaneously harvest energy. Each strut in the Stewart platform contains a moving electromagnet suspended between two fixed permanent magnets that are configured so that the magnet spring has both negative stiffness and soft nonlinearity. The use of stiffness nonlinearity improves vibration isolation efficiency. To obtain the frequency-response function for transmissibility and the power output in the first primary resonance, we apply the harmonic balance method, which is based on rigid-body dynamics and nonlinear elastic theory. The frequency response curves of the 6-dofs have peaks that redshift and bend leftward (toward lower frequencies), and a bubble-shaped resonance curve appears around the first resonance frequency. The numerical simulations support the analytical results. For various mechanical and electrical parameters, the analytical and numerical results both demonstrate that the frequency band of vibration isolation extends to lower frequencies and produces considerable power output. Moreover, the increase in energy harvesting leads to reduced vibration transmissibility under varying some parameters.Dynamics of a system of two coupled MEMS oscillatorshttps://zbmath.org/1487.740532022-07-25T18:03:43.254055Z"Rand, Richard H."https://zbmath.org/authors/?q=ai:rand.richard-h"Zehnder, Alan T."https://zbmath.org/authors/?q=ai:zehnder.alan-t"Shayak, B."https://zbmath.org/authors/?q=ai:shayak.b"Bhaskar, Aditya"https://zbmath.org/authors/?q=ai:bhaskar.adityaSummary: We investigate the dynamics of two limit cycle MEMS oscillators connected via spring coupling. Each individual oscillator is based on a MEMS structure which moves within a laser-driven interference pattern. As the structure vibrates, it changes the interference gap, causing the quantity of absorbed light to change, producing a feedback loop between the motion and the absorbed light and resulting in a limit cycle oscillation. A simplified model of this MEMS oscillator, omitting parametric feedback and structural damping, has been previously presented [the first three authors, ``Analysis of a simplified MEMS oscillator'', in: Proceedings of 9th European nonlinear dynamics conference, ENOC'17. Budapest: CongressLine Ltd. Article ID 77, 2 p. (2017)]. For the coupled system, a perturbation method is used to obtain a slow flow which is investigated using AUTO and numerical integration. Various bifurcations which occur as a result of changing the coupling strength are identified.
For the entire collection see [Zbl 1472.74004].Nonlinear dynamics of suspended cables under periodic excitation in thermal environments: two-to-one internal resonancehttps://zbmath.org/1487.740562022-07-25T18:03:43.254055Z"Zhao, Yaobing"https://zbmath.org/authors/?q=ai:zhao.yaobing"Lin, Henghui"https://zbmath.org/authors/?q=ai:lin.henghuiLove wave transference in piezomagnetic layered structure guided by an imperfect interfacehttps://zbmath.org/1487.740642022-07-25T18:03:43.254055Z"Goyal, Suman"https://zbmath.org/authors/?q=ai:goyal.suman"Sahu, Sanjeev A."https://zbmath.org/authors/?q=ai:sahu.sanjeev-anandSummary: The problem presents an analytical study of the wave transference in piezo-composite layer lying over an elastic substrate. The interface of the geometry is assumed to be imperfect. The imperfection is characterized by Linear Spring Model. Dynamics of the media taken are framed in form of direct Sturm-Liouville problem. Dispersion relations are found for both magnetically open and magnetically short case. Velocity profile of Love wave has been delineated through graphs for different affecting parameters (i.e., imperfection at the interface, layer thickness and heterogeneity in the substrate). It has been shown that the increase in these parameters increases the phase velocity of the Love wave. Further, layer thickness is noted to have a less effect on the velocity profile of the wave as compared to heterogeneity in the substrate. Moreover, a comparative study has been shown between the aforementioned cases with the variation in imperfect parameter. The velocity in open case is found to be higher than that of short case. The obtained results may provide guidance towards optimization of Surface Acoustic Wave devices and measurement of imperfections.Dispersion relations for localized waves of deformations in a water-saturated anisotropic layer between elastic half-spaceshttps://zbmath.org/1487.740662022-07-25T18:03:43.254055Z"Vyskub, V. G."https://zbmath.org/authors/?q=ai:vyskub.v-g"Glukhov, I. A."https://zbmath.org/authors/?q=ai:glukhov.i-a"Storozhev, V. I."https://zbmath.org/authors/?q=ai:storozhev.v-iSummary: A numerical-analytic solution of the problem of propagation of localized three-partial deformation waves in arbitrarily oriented direction in the plane of a saturated elastic-porous orthotropic layer contacting along the faces with the enclosing orthotropic half-spaces made of various elastic-porous materials is constructed. The general dispersion relation is obtained. A qualitative characteristic of the features of the asymptotic behavior of the velocities of the investigated wave motions in the high-frequency short-wave range for various orientation of the propagation
direction is given.Scattering of a plane sound waves by an elastic cylinder with an non-uniform coating situated near to a flat surfacehttps://zbmath.org/1487.740702022-07-25T18:03:43.254055Z"Tolokonnikov, Lev Alekseevich"https://zbmath.org/authors/?q=ai:tolokonnikov.lev-alekseevich"Efimov, Dmitriĭ Yur'evich"https://zbmath.org/authors/?q=ai:efimov.dmitrii-yurevichSummary: In article the problem of the scattering of an obliquely incident plane monochromatic sound wave by an elastic cylinder with a radially non-uniform elastic coating in presence of a flat surface (absolutely rigid and acoustically soft) is considered. The analytical solution of the problem by the method of imaginary sources using addition theorems for cylindrical wave functions is received. Wave fields in a containing medium and homogeneous elastic cylinder are found in the form of expansions in wave cylindrical functions. The boundary-value problem for the system of ordinary second order differential equations is constructed for determination of the displacement fields in inhomogeneous coatings.
Numerical calculations of frequency and angular characteristics of the scattered field for elastic homogeneous cylinders with and without coating located near the underlying plane are performed. Influence of continuously inhomogeneous elastic coatings on sound-reflecting properties of elastic cylindrical bodies are revealed.Transient response of a thermo-diffusive elastic thick circular plate with variable conductivity and diffusivityhttps://zbmath.org/1487.740762022-07-25T18:03:43.254055Z"Bajpai, Ankit"https://zbmath.org/authors/?q=ai:bajpai.ankit"Sharma, P. K."https://zbmath.org/authors/?q=ai:sharma.poonam-kumar"Kumar, Rajneesh"https://zbmath.org/authors/?q=ai:kumar.rajneeshSummary: This article describes the impacts of variable thermal conductivity and diffusivity on an infinite thermoelastic diffusion circular plate of finite width with a heat source due to axisymmetric thermal and chemical potential loadings in the light of two-temperature generalized thermoelastic diffusion theory. The thermal conductivity and diffusivity are assumed to be linear functions of thermodynamic temperature and concentration, respectively. The governing equations are transformed into the linear form by applying Kirchhoff's transform. These equations are solved by using the Laplace-Hankel transform technique. In the transformed region, the closed form expressions for conductive and thermodynamic temperatures, displacement and stress components, concentration, and chemical potential are obtained. To transform the solutions to the original domain, a numerical inversion technique is applied. Numerical results for thermodynamic and conductive temperatures, normal stress component, and chemical potential are depicted graphically to illustrate the impacts of two temperatures, ramping time parameter, variable thermal conductivity and diffusivity. A validation of the obtained results is also presented.Analysis of nonlinear deformation task of layered cylindrical shell by local surface force and temperature fieldhttps://zbmath.org/1487.740802022-07-25T18:03:43.254055Z"Abramidze, Ed."https://zbmath.org/authors/?q=ai:abramidze.edison"Abramidze, El."https://zbmath.org/authors/?q=ai:abramidze.eleneSummary: Based on one of the variants of improved theory, in the case of axisymmetric loading of layered cylindrical shell by local surface force and temperature field, for numerical solution of the nonlinear deformation task is obtained for this class the system of decision differential equations. \par A particular example of deformation of cylindrical shell is considered. It is given an appropriate analysis based on the results obtained from numerical realization of the example.Mathematical and asymptotic analysis of thermoelastic shells in normal damped response contacthttps://zbmath.org/1487.740822022-07-25T18:03:43.254055Z"Cao-Rial, M. T."https://zbmath.org/authors/?q=ai:cao-rial.m-t"Castiñeira, G."https://zbmath.org/authors/?q=ai:castineira.gonzalo"Rodríguez-Arós, Á."https://zbmath.org/authors/?q=ai:rodriguez-aros.angel-d"Roscani, S."https://zbmath.org/authors/?q=ai:roscani.sabrina-dSummary: The purpose of this paper is twofold. We first provide the mathematical analysis of a dynamic contact problem in thermoelasticity, when the contact is governed by a normal damped response function and the constitutive thermoelastic law is given by the Duhamel-Neumann relation. Under suitable hypotheses on data and using a Faedo-Galerkin strategy, we show the existence and uniqueness of solution for this problem. Then, we study the particular case when the deformable body is, in fact, a shell and use asymptotic analysis to study the convergence to a 2D limit problem when the thickness tends to zero.Thermomechanical waves in the elastic lithosphere-viscous asthenosphere systemhttps://zbmath.org/1487.740842022-07-25T18:03:43.254055Z"Lobkovsky, L. I."https://zbmath.org/authors/?q=ai:lobkovsky.l-i"Ramazanov, M. M."https://zbmath.org/authors/?q=ai:ramazanov.m-mSummary: The problem of the development of thermomechanical waves in the system consisting of two horizontal layers with rheology of a linearly elastic medium for the upper layer (lithosphere) and a viscous fluid for the lower layer (asthenosphere) is considered with regard to phase transition on their common boundary. The exact solution to the problem is found and its properties as functions of the parameters are studied. It is shown that for the characteristic physical parameters of the lithosphere and asthenosphere there exist solutions in the form of moderately damped strain tectonic waves and a geophysical interpretation of the results obtained is given.On the control of viscoelastic damped swelling porous elastic soils with internal delay feedbackshttps://zbmath.org/1487.740882022-07-25T18:03:43.254055Z"Apalara, Tijani A."https://zbmath.org/authors/?q=ai:apalara.tijani-abdulaziz"Yusuf, Moruf O."https://zbmath.org/authors/?q=ai:yusuf.moruf-o"Salami, Babatunde A."https://zbmath.org/authors/?q=ai:salami.babatunde-aSummary: We consider a swelling porous-elastic system with viscoelastic damping and delay feedbacks acting on the fluid equation. Using the multiplier method and under the well-known assumption on the weight of delay term, we unexpectedly establish a general decay result without imposing the usual condition of equal wave speeds of the system, unlike the case of Timoshenko and porous systems where damping on only one of the equations requires equal wave speeds propagation. Our coupling and the result give new contributions to the theory associated with asymptotic behaviors of swelling porous elastic soils.Mathematical regularities of the sliding friction process of a porous material based on iron impregnated with lubricating oil with dispersed particles of fluorinated graphenehttps://zbmath.org/1487.740912022-07-25T18:03:43.254055Z"Breki, Aleksandr Dzhalyul'evich"https://zbmath.org/authors/?q=ai:breki.aleksandr-dzhalyulevich"Chulkin, Sergeĭ Georgievich"https://zbmath.org/authors/?q=ai:chulkin.sergei-georgievich"Dobrovol'skiĭ, Nikolaĭ Mikhaĭlovich"https://zbmath.org/authors/?q=ai:dobrovolskii.n-m"Kuzovleva, Ol'ga Vladimirovna"https://zbmath.org/authors/?q=ai:kuzovleva.olga-vladimirovna"Gvozdev, Aleksandr Evgen'evich"https://zbmath.org/authors/?q=ai:gvozdev.aleksandr-evgenevich"Mazin, Evgeniĭ Vladimirovich"https://zbmath.org/authors/?q=ai:mazin.evgenii-vladimirovichSummary: The paper presents the results of a study of the sliding friction process of a porous material based on iron impregnated with lubricating oil with dispersed particles of fluorinated graphene. It is established that the regularities of the kinetics of external sliding friction have a sigmoidal and sigmoidal-linear character. Experimental results have been obtained showing that with an increase in the concentration of aggregates from flakes of fluorinated graphene in the lubricating oil, the average force and coefficient of friction decrease, while a good anti-friction effect is observed.Mathematical regularities of changes in the characteristics of the friction process of a porous composite material based on copper containing oil with graphene particleshttps://zbmath.org/1487.740932022-07-25T18:03:43.254055Z"Breki, Aleksandr Dzhalyul'evich"https://zbmath.org/authors/?q=ai:breki.aleksandr-dzhalyulevich"Chulkin, Sergeĭ Georgievich"https://zbmath.org/authors/?q=ai:chulkin.sergei-georgievich"Kolmakov, Alekseĭ Georg'evich"https://zbmath.org/authors/?q=ai:kolmakov.aleksei-georgevich"Kuzovleva, Ol'ga Vladimirovna"https://zbmath.org/authors/?q=ai:kuzovleva.olga-vladimirovna"Gvozdev, Aleksandr Evgen'evich"https://zbmath.org/authors/?q=ai:gvozdev.aleksandr-evgenevich"Mazin, Evgeniĭ Vladimirovich"https://zbmath.org/authors/?q=ai:mazin.evgenii-vladimirovich"Kuz'min, Alekseĭ Mikhaĭlovich"https://zbmath.org/authors/?q=ai:kuzmin.aleksei-mikhailovichSummary: The paper presents the results of a study of the sliding friction processes of a porous copper-based material impregnated with lubricating oil with dispersed particles of fluorinated graphene. Mathematical regularities of changes in the characteristics of the friction interaction are established. It is shown that the regularities of changes in the average friction force have a sigmoid-step character. Experimental results have been obtained showing that with an increase in the concentration of aggregates from flakes of fluorinated graphene in the lubricating oil, the average friction force and coefficient of friction decrease, while a good anti-friction effect is observed. It is shown that the average work of the friction force, and consequently the energy losses due to friction, when adding 0.01\% of aggregates from fluorinated graphene flakes to the lubricating oil decreases by 3721 j, and when adding 0.1\% by 4098 j. It was found that the average coefficient of friction when adding 0.01\% of fluorinated graphene flake aggregates to the lubricating oil decreases by 27\%, and when adding 0.1\% by 30\%.A bi-potential contact formulation of orthotropic adhesion between soft bodieshttps://zbmath.org/1487.740972022-07-25T18:03:43.254055Z"Hu, L. B."https://zbmath.org/authors/?q=ai:hu.liangbing|hu.leibo|hu.liang-bo|hu.liangbin|hu.lianbo"Cong, Y."https://zbmath.org/authors/?q=ai:cong.yuan|cong.yirui|cong.yan|cong.yang|cong.yuhao|cong.yuancai|cong.yongzheng|cong.yulai|cong.yunyue|cong.yu|cong.yue"Renaud, C."https://zbmath.org/authors/?q=ai:renaud.christophe|renaud.christine"Feng, Z.-Q."https://zbmath.org/authors/?q=ai:feng.zhiqin|feng.ziqin|feng.zhouquan|feng.zhiqiang|feng.zi-qiang|feng.zhiquanSummary: An orthotropic adhesion model is proposed based on the bi-potential method to solve adhesive contact problems with orthotropic interface properties between hyperelastic bodies. The model proposes a straightforward description of interface adhesion with orthotropic adhesion stiffness, whose components are conveniently expressed according to the local coordinate system. Based on this description, a set of extended unilateral and tangential contact laws has been formulated. Furthermore, we use an element-wise scalar parameter \(\beta\) to characterize the strength of interface adhesive bonds, and the effects of damage. Therefore, complete cycles of bonding and de-bonding of adhesive links with the account for orthotropic interface effects can be modelled. The proposed model has been tested on cases involving both tangential and unilateral contact kinematics. The test cases allowed emergence of orthotropic interface effects between elastomer bodies involving hyperelasticity. Meanwhile, the model can be implemented with minimum effort, and provides inspiration for the modelling of adhesive interface effects in areas of applications such as biomechanics.Models of plane fractures expansionhttps://zbmath.org/1487.741092022-07-25T18:03:43.254055Z"Khabirov, S. V."https://zbmath.org/authors/?q=ai:khabirov.salavat-valeevich"Khabirov, S. S."https://zbmath.org/authors/?q=ai:khabirov.s-sSummary: Approximate models of crack opening in the reservoir under the action of the filtered fluid are derived. The cross-sections of the fracture are assumed to be plane-parallel and have a small thickness. The models are based on exact solutions of the equations for viscous fluid motion including invariant solutions. Filtration of a fluid through a moving boundary, the absence of a tangential motion at the boundary, and elastic forces compressing the crack are taken into account.Calculation of critical depth of edge crack in the main oil pipeline in the neighborhood of a transverse welded jointhttps://zbmath.org/1487.741102022-07-25T18:03:43.254055Z"Pokrovskiy, A. M."https://zbmath.org/authors/?q=ai:pokrovskiy.a-m"Dubovitskiy, E. I."https://zbmath.org/authors/?q=ai:dubovitskiy.e-i"Chermoshentseva, A. S."https://zbmath.org/authors/?q=ai:chermoshentseva.a-sSummary: A numerical method for calculating the critical depth of an edge semi-elliptical crack in the main oil pipeline in the zone of a transverse weld was developed. To calculate the structural composition of steel after welding and the residual welding stresses is used the author-developed finite element software package in Fortran Visual environment. The nonlinear nonstationary heat conductivity problem was solved by the finite difference method using the boundary conditions of third kind. Modeling of the kinetics of conversion of austenite to ferrite and bainite under nonisothermal conditions during welding was carried out based on the theory of isokinetic reactions. The calculation of the residual welding stress is performed by solving the problem of thermoelastic plasticity using the finite element method for material with nonstationary structure. The calculation of the crack resistance is based on Irwin's force failure criterion, and the dependence of the failure viscosity on the structural composition is considered. The ANSYS finite element software was used for calculating the maximum stress intensity factor along the edge of an edge semi-elliptical longitudinal crack in the pipeline. The distribution of fracture toughness as a function of the distance to the weld center is presented, as well as the results of crack resistance analysis in the form of dependences of the critical crack depth on the distance to the middle of the weld and the ratio of the crack half-length to its depth.On the role of added mass and vorticity release for self-propelled aquatic locomotionhttps://zbmath.org/1487.760142022-07-25T18:03:43.254055Z"Paniccia, D."https://zbmath.org/authors/?q=ai:paniccia.d"Graziani, G."https://zbmath.org/authors/?q=ai:graziani.giorgio"Lugni, C."https://zbmath.org/authors/?q=ai:lugni.claudio"Piva, R."https://zbmath.org/authors/?q=ai:piva.renzoSummary: Aquatic locomotion of a deformable body from rest up to its asymptotic speed is given by the unsteady motion which is produced by a series of periodic reactions dictated by the body configuration and by the style of swimming. The added mass plays a crucial role, not only for the initial burst, but also along each manoeuvre, to accelerate the surrounding fluid for generating the kinetic energy and to enable vortex shedding in the wake. The estimate of these physical aspects has been largely considered in most theoretical models, but not sufficiently deepened in many experimental and numerical investigations. As a motivation, while the vortical structures are easily detectable from the flow field, the added mass, on the contrary, is usually embedded in the overall forcing terms. By the present impulse formulation, we are able to separate and to emphasize the role of the added mass and vorticity release to evaluate in a neat way their specific contributions. The precise identification of the added mass is also instrumental for a well-posed numerical problem and for easily readable results. As a further point, the asymptotic speed is found to be guided either by the phase velocity of the prescribed undulation and by the unavoidable recoil motion induced by the self-propelled swimming. The numerical results reported in the present paper concern simplified cases of non-diffusing vorticity and two-dimensional flow.Use of Galerkin technique to the rolling of a plate in deep waterhttps://zbmath.org/1487.760192022-07-25T18:03:43.254055Z"Ray, Swagata"https://zbmath.org/authors/?q=ai:ray.swagata"De, Soumen"https://zbmath.org/authors/?q=ai:de.soumen"Mandal, B. N."https://zbmath.org/authors/?q=ai:mandal.birendra-nathSummary: The classical problems of surface water waves produced by small oscillations of a thin vertical plate partially immersed as well as submerged in deep water are reinvestigated here. Each problem is reduced to an integral equation involving horizontal component of velocity across the vertical line outside the plate. The integral equations are solved numerically using Galerkin approximation in terms of simple polynomials multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge(s) of the plate. Fairly accurate numerical estimates for the amplitude of the radiated wave at infinity due to rolling and also for swaying of the pate in each case are obtained and these are depicted graphically against the wave number for various cases.An efficient and generalized solid boundary condition for SPH: applications to multi-phase flow and fluid-structure interactionhttps://zbmath.org/1487.760602022-07-25T18:03:43.254055Z"Zhang, Chi"https://zbmath.org/authors/?q=ai:zhang.chi"Zhu, Yujie"https://zbmath.org/authors/?q=ai:zhu.yujie"Lyu, Xiuxiu"https://zbmath.org/authors/?q=ai:lyu.xiuxiu"Hu, Xiangyu"https://zbmath.org/authors/?q=ai:hu.xiangyuSummary: In this paper, we generalize the solid boundary condition where a one-sided Riemann solver is introduced to determine the fluid-solid interaction for weakly compressible smoothed particle hydrodynamics (SPH) presented in [\textit{C. Zhang} et al., J. Comput. Phys. 337, 216--232 (2017; Zbl 1415.76514)] to model multi-phase flows with large density ratio and multi-phase fluid-structure interaction (FSI) in multi-resolution scenario. Compared with the boundary condition proposed by \textit{S. Adami} et al. [``A generalized wall boundary condition for smoothed particle hydrodynamics'', J. comput. Phys. 231--21, 7057--7075 (2012; \url{doi:10.1016/j.jcp.2012.05.005})] where solid is discretized by dummy particles whose physical quantities are extrapolated from surrounding fluid particles, the present method is very simple and efficient as extra extrapolation is avoided by constructing a one-sided Riemann problem for each interacting fluid-solid particle pair. This feature makes its extension to multi-phase flow and FSI straightforward. Furthermore, we adopt a penalty method in multi-resolution discretization to prevent particle penetration in violent multi-phase simulation. A set of examples involving multi-phase flows with high density ratio and complex interface, and multi-phase FSI are studied to demonstrate the accuracy, robustness and versatility of the present method. The validations presented herein and those reported by Zhang et al. [loc. cit.] where free-surface flows exhibiting violent events such as impact and breaking are studied indicate that the present method provides a unified approach for addressing the solid, i.e., rigid and flexible, boundary condition in multi-physics SPH applications.Dynamic simulations of an encapsulated microbubble translating in a tube at low capillary and Reynolds numbershttps://zbmath.org/1487.760942022-07-25T18:03:43.254055Z"Vlachomitrou, M."https://zbmath.org/authors/?q=ai:vlachomitrou.m"Lytra, A."https://zbmath.org/authors/?q=ai:lytra.a"Pelekasis, N."https://zbmath.org/authors/?q=ai:pelekasis.nikos-a|pelekasis.nikolaos-aSummary: The dynamic translation of a micron-sized encapsulated bubble is investigated numerically inside a horizontal tube where liquid flows under constant pressure drop, when the effect of gravity is neglected. The coating of the bubble is treated as an infinitesimally thin viscoelastic shell with bending resistance. The Galerkin Finite Element Methodology is employed to solve the axisymmetric flow configuration combined with the spine or elliptic mesh generation techniques for updating the mesh. The microbubble is initially elongated and the Reynolds number of the flow is relatively small, i.e. \(\operatorname{Re}< 5\). Benchmark simulations for long free bubbles robustly recover the scaling of the film thickness with the 2/3 power of the capillary number based on surface tension. In the case of encapsulated bubbles, for a sufficiently small capillary number and after a short transient period, the bubble acquires a Bretherton type shape that slowly expands in order to accommodate changes in the liquid pressure. The speed of translation is nearly constant, close to the mean velocity of the flow, and does not depend on surface tension, shell elasticity or bending resistance. Fluid motion in the thin film ``contact'' region that forms in the gap between the tube and the shell is seen to be a stable flow arrangement that entails a mixture of pressure driven and shear driven flow, with the latter greatly affected by the area dilatation modulus via the tangential stress balance. By introducing a modified capillary number based on the area dilatational modulus, rather than surface tension, it is seen that the dimensionless film thickness that occupies the region between the bubble and the tube wall increases with the 1/3 power of the modified capillary number with increasing area dilatation. Simulations when surface tension is absent indicate that tangential shear generated due to variation of the membrane stress in the transition region that joins the bulk of the flow configuration with the contact region, leads to film thinning via the 5/7 power of the modified capillary number. Variations in the transverse shear of the viscoelastic shell generate large lubrication overpressures in the thin film region between the tube and the shell that are exerted radially on the shell and are conjectured to be responsible for the onset of 3d buckled shapes. The latter are often observed experimentally in similar flow configurations of capsules and are characterized by wrinkles that develop in the azimuthal direction around the shell equator.An energy approach to the calculation of forces acting on solid bodies in ferrofluidshttps://zbmath.org/1487.780032022-07-25T18:03:43.254055Z"Ivanov, A. S."https://zbmath.org/authors/?q=ai:ivanov.aleksandr-sSummary: The main advantages of the energy approach to solving the problem of determining magnetic forces acting on solid bodies immersed into magnetized ferrofluids (FFs) are shown. Characteristic disadvantages of the standard approach to the calculation of magnetic forces using the Bernoulli equation for FFs and an equation for the magnetic pressure jump at the interface are considered. A review of works devoted to the study of forces acting on solid bodies immersed in magnetized FFs is presented. This literature review convincingly demonstrates the need for and potential advantage of using the energy approach to these problems, since the analytical expressions significantly depend on the body shape and obtaining the final numerical results is complicated by the error of magnetic field calculation at the ``solid body-FF'' interface where the normal component of induction and the tangential component of the magnetic field exhibit a discontinuity. In contrast, the energy approach allows using the standard functions of program packages for determining thermodynamic potentials. The choice of a thermodynamic potential correctly describing experimental data is discussed. The method of magnetic energy determination is justified by the problem setting and verified by comparison of the results of several numerical solutions obtained using the open software package FEMM for FFs obeying a nonlinear magnetization law. This analysis was previously performed neither experimentally nor theoretically in view of the commonly accepted use of simplifying assumptions (approximations of weak and strong magnetic fields or a noninductive approximation). Here, the energy approach to determining forces acting on solid bodies in FFs has been justified by pairwise comparison of the results obtained in the framework of this approach to the data of laboratory experiment and the results of standard calculations.Nonstationary thermokinetic model of surface laser scanninghttps://zbmath.org/1487.800082022-07-25T18:03:43.254055Z"Knyazeva, A. G."https://zbmath.org/authors/?q=ai:knyazeva.anna-georgievnaSummary: This paper presents a thermophysical model of laser beam scanning of the surface of a two-layer plate whose top layer melts and undergoes shrinkage due to changes in porosity and whose bottom layer (substrate) does not melt. The dependences of the heat capacity, thermal conductivity, and reflection coefficient on porosity are taken into account. Heat loss can occur by both radiation and convection. Results illustrating the non-stationarity of the process throughout the scan are presented. It is shown that the complex thermal cycles and inhomogeneous temperature field are directly related to inhomogeneous shrinkage, leading to the surface topography typical of selective laser melting processes.An analytical model for effective thermal conductivity of the media embedded with fracture networks of power law length distributionshttps://zbmath.org/1487.800102022-07-25T18:03:43.254055Z"Miao, Tongjun"https://zbmath.org/authors/?q=ai:miao.tongjun"Chen, Aimin"https://zbmath.org/authors/?q=ai:chen.aimin"Jiang, Lijuan"https://zbmath.org/authors/?q=ai:jiang.lijuan"Zhang, Huajie"https://zbmath.org/authors/?q=ai:zhang.huajie"Liu, Junfeng"https://zbmath.org/authors/?q=ai:liu.junfeng"Yu, Boming"https://zbmath.org/authors/?q=ai:yu.bomingDirac structures in thermodynamics of non-simple systemshttps://zbmath.org/1487.800132022-07-25T18:03:43.254055Z"Yoshimura, Hiroaki"https://zbmath.org/authors/?q=ai:yoshimura.hiroaki"Gay-Balmaz, François"https://zbmath.org/authors/?q=ai:gay-balmaz.francoisSummary: We present the Dirac structures and the associated Dirac system formulations for \textit{non-simple} thermodynamic systems by focusing upon the cases that include irreversible processes due to friction and heat conduction. These systems are called non-simple since they involve several entropy variables. We review the variational formulation of the evolution equations of such non-simple systems. Then, based on this, we clarify that there exists a Dirac structure on the Pontryagin bundle over a thermodynamic configuration space and we develop the Dirac dynamical formulation of such non-simple systems. The approach is illustrated with the example of an adiabatic piston.
For the entire collection see [Zbl 1482.94007].Thermomechanical effects of radiation origin in microelectronics productshttps://zbmath.org/1487.800162022-07-25T18:03:43.254055Z"Volkov, Yu. A."https://zbmath.org/authors/?q=ai:volkov.yurii-aleksandrovich"Vyrostkov, M. Yu."https://zbmath.org/authors/?q=ai:vyrostkov.m-yu"Markov, M. B."https://zbmath.org/authors/?q=ai:markov.mikhail-b"Tarakanov, I. A."https://zbmath.org/authors/?q=ai:tarakanov.ilya-alekseevichSummary: A mathematical model of the thermomechanical effect of penetrating radiation on a microelectronic product is presented. The model is based on the thermoelasticity equations, which are a consequence of the quantum kinetic equations for phonons. Heat transport is described by the law of conservation of energy and the Cattaneo equation, which takes into account the finite rate of heat propagation. Lattice vibrations are considered in the approximation of the linear theory of elasticity. In general, the model determines the distribution of temperature, energy flow, deformation and stress. Difference schemes have been developed for solving the model equations. The effectiveness of the developed model was tested by solving the problem of thermal shock.Robust and fast excitation fluctuations transfer between two membranes in an optomechanical systemhttps://zbmath.org/1487.810232022-07-25T18:03:43.254055Z"Zhang, Chun-Ling"https://zbmath.org/authors/?q=ai:zhang.chunling"Chen, Xiang"https://zbmath.org/authors/?q=ai:chen.xiang"Liao, Chang-Geng"https://zbmath.org/authors/?q=ai:liao.chang-geng"Lin, Xiu-Min"https://zbmath.org/authors/?q=ai:lin.xiu-minSummary: The quantum state control or entanglement preparation for macroscopic matter is an attractive research. Optomechanical system provides an ideal platform to observe the quantum behaviors of macroscopic matter. In this paper, we present a scheme to implement the average excitation fluctuations transfer between two membranes in an optomechanical system via shortcut to adiabatic passage which is based on transitionless quantum driving. In order to quickly attain the transfer, we choose a suitable evolution path and optimize the experimental parameters. Numerical simulation demonstrates that the proposed scheme is robust against membrane damping and cavity decay. Furthermore, this idea can be used to generate entanglement of two membrane modes in a short time. Finally, we also discuss the experimental implementation of this scheme. This work may provide a new method for generating the macroscopic superposition state in the optomechanical system.Gravitational decoupling algorithm modifies the value of the conserved charges and thermodynamics properties in Lovelock unique vacuum theoryhttps://zbmath.org/1487.830882022-07-25T18:03:43.254055Z"Estrada, Milko"https://zbmath.org/authors/?q=ai:estrada.milkoSummary: We provide an extension of the Gravitational Decoupling (algorithm) for the Lovelock theory with Unique Vacuum (LUV), which represents a simple way to solve the equations of motion. Due to the application of this algorithm, the energy of the system splits in the \textit{energy of the seed solution} and the \textit{energy of each quasi-LUV sector}. Under certain assumptions imposed, the total energy varies due to the contribution of energy of each quasi-LUV sector. It is provided a new solution, whose energy differs from the energy of the seed solution in a quantity that depends on the number of extra sources. The new solution has two inner horizons, which is a proper characteristic of itself. Furthermore, its thermodynamics differs from the seed solution, since our solution is always stable and does not have phase transitions. Since the first law of thermodynamics is modified by the presence of the matter fields, we provide a new version of the first law for LUV, where a local definition of the variation of energy is defined, and, where the entropy and temperature are consistent for LUV theory.Computation of new degree-based topological indices of graphenehttps://zbmath.org/1487.920652022-07-25T18:03:43.254055Z"Shigehalli, V. S."https://zbmath.org/authors/?q=ai:shigehalli.v-s"Kanabur, Rachanna"https://zbmath.org/authors/?q=ai:kanabur.rachannaSummary: Graphene is one of the most promising nanomaterials because of its unique combination of superb properties, which opens a way for its exploitation in a wide spectrum of applications ranging from electronics to optics, sensors, and biodevices. Inspired by recent work on Graphene of computing topological indices, here we propose new topological indices, namely, Arithmetic-Geometric index (AG\(_1\) index), SK index, SK\(_1\) index, and SK\(_2\) index of a molecular graph \(G\) and obtain the explicit formulae of these indices for Graphene.