Recent zbMATH articles in MSC 74H45https://zbmath.org/atom/cc/74H452021-05-28T16:06:00+00:00WerkzeugInfluence of a moving mass on the dynamic behaviour of viscoelastically connected prismatic double-Rayleigh beam system having arbitrary end supports.https://zbmath.org/1459.740642021-05-28T16:06:00+00:00"Abiodun Gbadeyan, Jacob"https://zbmath.org/authors/?q=ai:abiodun-gbadeyan.jacob"Akangbe Hammed, Fatai"https://zbmath.org/authors/?q=ai:akangbe-hammed.fataiSummary: This paper deals with the lateral vibration of a finite double-Rayleigh beam system having arbitrary classical end conditions and traversed by a concentrated moving mass. The system is made up of two identical parallel uniform Rayleigh beams which are continuously joined together by a viscoelastic Winkler type layer. Of particular interest, however, is the effect of the mass of the moving load on the dynamic response of the system. To this end, a solution technique based on the generalized finite integral transform, modified Struble's method, and differential transform method (DTM) is developed. Numerical examples are given for the purpose of demonstrating the simplicity and efficiency of the technique. The dynamic responses of the system are presented graphically and found to be in good agreement with those previously obtained in the literature for the case of a moving force. The conditions under which the system reaches a state of resonance and the corresponding critical speeds were
established. The effects of variations of the ratio \((\gamma_1)\) of the mass of the moving load to the mass of the beam on the dynamic response are presented. The effects of other parameters on the dynamic response of the system are also examined.Another special case of vibrations of a rolling tire.https://zbmath.org/1459.740682021-05-28T16:06:00+00:00"Kozhevnikov, I. F."https://zbmath.org/authors/?q=ai:kozhevnikov.ivan-fSummary: We investigate a special case of vibrations of a loaded tire rolling at constant speed. A previously proposed analytical model of a radial tire is considered [the author, Nelineĭn. Din. 15, No. 1, 67--78 (2019; Zbl 1451.74103)]. The surface of the tire is a flexible tread combined with elastic sidewalls. In the undeformed state, the tread is a circular cylinder. The tread is reinforced with inextensible cords. The tread is the part of the tire that makes actual contact with the ground plane. In the undeformed state, the sidewalls are represented by parts of two tori and consist of incompressible rubber described by the Mooney-Rivlin model. The previously obtained partial differential equation which describes the tire radial in-plane vibrations about steady-state regime of rolling is investigated. Analyzing the discriminant of the quartic polynomial, which is the function of the frequency of the tenth degree and the function of the angular velocity of the sixth degree, the rare case of a root of multiplicity three is discovered. The angular velocity of rotation, the tire speed and the natural frequency, corresponding to this case, are determined analytically. The mode shape of vibration in the neighborhood of the singular point is determined analytically.Differential quadrature procedure for in-plane vibration analysis of variable thickness circular arches traversed by a moving point load.https://zbmath.org/1459.740652021-05-28T16:06:00+00:00"Eftekhari, S. A."https://zbmath.org/authors/?q=ai:eftekhari.s-aboozarSummary: Point discretization methods such as the differential quadrature method (DQM) are well known to have difficulties in solving partial differential equations that involve the Dirac-delta function because the Dirac-delta function is a generalized singularity function and it cannot be discretized directly using the DQM. To overcome this difficulty, a simple differential quadrature methodology is proposed in this study, where the Dirac-delta function is expanded into a Fourier trigonometric series. By expanding the Dirac-delta function into a Fourier trigonometric series, this singular function is treated as non-singular functions, which can be discretized easily and directly using the DQM. The applicability of the proposed method is demonstrated by the in-plane vibration analysis of variable thickness circular arches traversed by a moving point load. The numerical results show that the proposed method is highly accurate and reliable.A simplified analytical solution of mechanical responses of soil subjected to repeated impact loading.https://zbmath.org/1459.741302021-05-28T16:06:00+00:00"Zhao, Futian"https://zbmath.org/authors/?q=ai:zhao.futian"Liu, Jun"https://zbmath.org/authors/?q=ai:liu.jun.1|liu.jun.5|liu.jun.4|liu.jun.2|liu.jun|liu.jun.3"Xiao, Zhimin"https://zbmath.org/authors/?q=ai:xiao.zhimin"Liu, Mingqing"https://zbmath.org/authors/?q=ai:liu.mingqing"Wang, Yue"https://zbmath.org/authors/?q=ai:wang.yue.1|wang.yue.3|wang.yue.2"Ou, Chen"https://zbmath.org/authors/?q=ai:ou.chen"Zhen, Mengyang"https://zbmath.org/authors/?q=ai:zhen.mengyangSummary: A simplified dynamic response model is proposed based on the deformation and dynamic stress response characteristics of soil under impact loading. The foundation is divided into two distinct zones: a projection cylinder acting vertically under impact loading and a hollow cylinder outside the projection area. It is assumed that the ramming deformation of the projected cylinder under the vertical impact load is a quasi-static loading process under the maximum contact dynamic stress through the quasi-static method, and the settlement calculation without lateral deformation is given. It is assumed that the inner wall of the hollow cylinder is subjected to horizontal lateral pressure and the analytical solution of the horizontal dynamic stress considering the plastic deformation of soil is given. The simplified dynamic response model can reflect the mechanical response of soil under impulse train load well which can provide reference for similar projects.Influence of vibrational excitation of the gas on the position of the laminar-turbulent transition region on a flat plate.https://zbmath.org/1459.760582021-05-28T16:06:00+00:00"Grigoryev, Yu. N."https://zbmath.org/authors/?q=ai:grigorev.yu-n"Ershov, I. V."https://zbmath.org/authors/?q=ai:ershov.i-vSummary: The influence of thermal nonequilibrium on the laminar-turbulent transition is studied with the use of the \(\mathrm{e}^N\) -method for two widespread flow regimes in a supersonic boundary layer at the Mach number \(\mathrm{M}=4.5\) . The set of the actual frequencies of spatial disturbances is determined on the basis of the neutral curves for temporal disturbances. Families of the curves of \(N\) -factors are calculated for selected frequencies. Then, based on the envelopes of these curves, the transition Reynolds number \(\mathrm{Re}_{\delta T}\) for a given transition factor \(N_T\) is determined. The calculations show that the transition region in the case with \(N_T=8\) and vibrational excitation level below the dissociation limit is located 12--14\% downstream as compared to the transition region in a perfect gas.Determination of damping properties of an elongated plate with an integral damping coating on the base of studying complex eigenfrequencies.https://zbmath.org/1459.740722021-05-28T16:06:00+00:00"Paimushin, V. N."https://zbmath.org/authors/?q=ai:paimushin.vitaliy-n"Firsov, V. A."https://zbmath.org/authors/?q=ai:firsov.v-a"Shishkin, V. M."https://zbmath.org/authors/?q=ai:shishkin.v-mSummary: We describe the structure of a perspective integral damping coating consisting (with respect to the thickness) of two layers of a viscoelastic material with a thin reinforcing layer in-between. We propose a four-layer finite element model with fourteen degrees of freedom for a plate with a mentioned damping coating. This model allows us to take into account the effect of transversal compression of damping layers under high-frequency vibrations of the plate. For determining some lower complex modes and frequencies of free vibrations of the damped plate, we solve a generalized complex eigenvalue problem using the method of iterations in a subspace.Galloping stability and wind tunnel test of iced quad bundled conductors considering wake effect.https://zbmath.org/1459.740692021-05-28T16:06:00+00:00"Liu, Xiaohui"https://zbmath.org/authors/?q=ai:liu.xiaohui"Zou, Ming"https://zbmath.org/authors/?q=ai:zou.ming"Wu, Chuan"https://zbmath.org/authors/?q=ai:wu.chuan"Cai, Mengqi"https://zbmath.org/authors/?q=ai:cai.mengqi"Min, Guangyun"https://zbmath.org/authors/?q=ai:min.guangyun"Yang, Shuguang"https://zbmath.org/authors/?q=ai:yang.shuguangSummary: A new quad bundle conductor galloping model considering wake effect is proposed to solve the problem of different aerodynamic coefficients of each subconductor of iced quad bundle conductor. Based on the quasistatic theory, a new 3-DOF (three degrees of freedom) galloping model of iced quad bundle conductors is established, which can accurately reflect the energy transfer and galloping of quad bundle conductor in three directions. After a series of formula derivations, the conductor stability judgment formula is obtained. In the wind tunnel test, according to the actual engineering situation, different variables are set up to accurately simulate the galloping of iced quad bundle conductor under the wind, and the aerodynamic coefficient is obtained. Finally, according to the stability judgment formula of this paper, calculate the critical wind speed of conductor galloping through programming. The dates of wind tunnel test and calculation in this paper can be used in the antigalloping design of transmission lines.Vibration analysis of piezoelectric composite plate resting on nonlinear elastic foundations using sinc and discrete singular convolution differential quadrature techniques.https://zbmath.org/1459.740762021-05-28T16:06:00+00:00"Ragb, Ola"https://zbmath.org/authors/?q=ai:ragb.ola"Salah, Mohamed"https://zbmath.org/authors/?q=ai:salah.mohamed-ben|salah.mohamed-essalah"Matbuly, M. S."https://zbmath.org/authors/?q=ai:matbuly.m-s"Amer, R. B. M."https://zbmath.org/authors/?q=ai:amer.r-b-mSummary: In this work, free vibration of the piezoelectric composite plate resting on nonlinear elastic foundations is examined. The three-dimensionality of elasticity theory and piezoelectricity is used to derive the governing equation of motion. By implementing two differential quadrature schemes and applying different boundary conditions, the problem is converted to a nonlinear eigenvalue problem. The perturbation method and iterative quadrature formula are used to solve the obtained equation. Numerical analysis of the proposed schemes is introduced to demonstrate the accuracy and efficiency of the obtained results. The obtained results are compared with available results in the literature, showing excellent agreement. Additionally, the proposed schemes have higher efficiency than previous schemes. Furthermore, a parametric study is introduced to investigate the effect of elastic foundation parameters, different materials of sensors and actuators, and elastic and geometric characteristics of the composite plate on the natural frequencies and mode shapes.A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams.https://zbmath.org/1459.740592021-05-28T16:06:00+00:00"Eltaher, M. A."https://zbmath.org/authors/?q=ai:eltaher.mohamed-a"Khater, M. E."https://zbmath.org/authors/?q=ai:khater.m-e"Emam, Samir A."https://zbmath.org/authors/?q=ai:emam.samir-aSummary: The enabling emerging technologies such as nanotechnology increased the demand for small-size devices. The proper understanding of the nonclassical behavior of nanostructures is key for the design of these devices. As a result, the static and dynamic behavior of nanoscale beam structures has received a great attention in the past few years. This review aims at directing the light to research work concerned with bending, buckling, vibrations, and wave propagation of nanobeams modeled according to the nonlocal elasticity theory of Eringen. Due to the large body of references found in the literature, the authors chose to briefly present the key findings and challenges and direct light to possible future work. This review does not intersect with recent relevant reviews, which reflects its significance to readers.Vibration control of beams subjected to a moving mass using a successively combined control method.https://zbmath.org/1459.740752021-05-28T16:06:00+00:00"Pi, Yangjun"https://zbmath.org/authors/?q=ai:pi.yangjun"Ouyang, Huajiang"https://zbmath.org/authors/?q=ai:ouyang.huajiangSummary: This study addresses the vibration control of beams subjected to a moving mass, which represent real applications such as vehicle-bridge interaction. Positive position feedback control (PPF) which has been successfully used in vibration control of flexible structures is found not suitable for the current control problem when the moving mass is travelling on the beam as it makes the structure more flexible but is found capable of reducing free vibration after the moving mass leaves the beam. Sliding mode control (SMC) is known to be a robust method to deal with parameter uncertainties and disturbances in vibration, however it is found to be likely to introduce some higher-frequency vibration which is detrimental to the beam. A method combining SMC and PPF is proposed to suppress the vibration of the beam when the moving mass is on and off the beam, which overcomes the above problems and possesses the benefits of both SMC control and PPF control. Simulated numerical examples demonstrate the effectiveness of the proposed method.Free and forced vibrations of double-layered viscoelastic orthotropic graphene sheets with a high-order surface stress effect.https://zbmath.org/1459.740732021-05-28T16:06:00+00:00"Pang, M."https://zbmath.org/authors/?q=ai:pang.mingxian|pang.mingbao|pang.meiling|pang.meng|pang.miao|pang.myungyull|pang.mengjuan|pang.mingyong|pang.min|pang.maoxiu|pang.mao|pang.muye"Fang, Y."https://zbmath.org/authors/?q=ai:fang.yixiang|fang.yuanqiao|fang.youjian|fang.yiming|fang.yinfeng|fang.yuda|fang.yuanxia|fang.yujuan|fang.yaoli|fang.yukun|fang.yuguang|fang.yiqi|fang.yan|fang.yuquang|fang.yong.1|fang.youkang|fang.yuping|fang.yonglei|fang.yanan|fang.yayun|fang.yuefa|fang.yixin|fang.yilin|fang.ying|fang.yinhai|fang.yongchun|fang.yunlan|fang.yuntuan|fang.yu|fang.yingjue|fang.yixian|fang.yajun|fang.yanjun|fang.yanxian|fang.yuming|fang.yaner|fang.yang|fang.yaquan|fang.yi|fang.yizhou|fang.yanling|fang.yechang|fang.yunmei|fang.yichuan|fang.yongfei|fang.yuqiang|fang.yuan|fang.yaping|fang.yibin|fang.yuwei|fang.yong.2|fang.yujie|fang.youtong|fang.ye|fang.yaling|fang.yiyuan|fang.yuhan|fang.yikai|fang.yujing|fang.yile|fang.yanning|fang.yangqin|fang.yamin|fang.yangwang|fang.yanxiang|fang.yanbing|fang.yuke|fang.yuejian|fang.yunfei|fang.yue|fang.yiwei|fang.yong|fang.yuzhi|fang.yanqin|fang.yanyan|fang.yao|fang.yanmei|fang.yingguang|fang.yuwen|fang.yihao|fang.yun|fang.yuzhuo"Zhang, Y. Q."https://zbmath.org/authors/?q=ai:zhang.yongquan|zhang.yongqi.1|zhang.yanqiong|zhang.youqiang|zhang.yunqing|zhang.yuanqiao|zhang.yuqin|zhang.yuqiong|zhang.yanqi|zhang.yuquan|zhang.yaqiu|zhang.yong-qian|zhang.yuanqi|zhang.yeqiang|zhang.yongqiang|zhang.yaqing|zhang.yaqiong|zhang.yaqi|zhang.yiqi|zhang.yaqin|zhang.yingqi|zhang.yaqian|zhang.ye-qi|zhang.yingqian|zhang.yanqiu|zhang.yuanqing|zhang.yiqing|zhang.yiqun|zhang.yueqin|zhang.yunqi|zhang.yunqin|zhang.youqian|zhang.yan-qing|zhang.yongqian|zhang.yuqian|zhang.yongqin|zhang.yingqing|zhang.you-qing|zhang.yiqiang|zhang.yunquan|zhang.ying-qiao|zhang.yanqiang|zhang.yongqing|zhang.yunqing.1|zhang.yuqi|zhang.yuqing|zhang.yuqiang|zhang.yanqiao|zhang.yunqiu|zhang.yuanquanSummary: Transverse vibrations of a double-layered viscoelastic orthotropic graphene sheet system are investigated. The two sheets in the system are coupled by the visco-Pasternak medium. General governing equations for free and forced vibrations of the double-layered graphene sheet system with a high-order surface stress effect are formulated. Theoretical solutions for the damped vibrational frequency, damping ratio, and relative deflection of the two sheets with simply supported boundary conditions are obtained. The effects of the high-order surface stress on the damped frequency and damping ratio of the system for in-phase and out-of-phase free vibrations are discussed. The impacts of the high-order surface stress, structural damping, medium damping, Winkler modulus, and shear modulus of the medium on the relative deflection of the two sheets for forced vibrations are investigated. It is demonstrated that the high-order surface stress effects on the vibrational properties of the system are more significant than those of the conventional surface stress.Vibrational energy flow model for a high damping beam with constant axial force.https://zbmath.org/1459.740782021-05-28T16:06:00+00:00"Teng, Xiaoyan"https://zbmath.org/authors/?q=ai:teng.xiaoyan"Liu, Nan"https://zbmath.org/authors/?q=ai:liu.nan"Xudong, Jiang"https://zbmath.org/authors/?q=ai:xudong.jiangSummary: The energy flow analysis (EFA) method is developed to predict the energy density of a high damping beam with constant axial force in the high-frequency range. The energy density and intensity of the beam are associated with high structural damping loss factor and axial force and introduced to derive the energy transmission equation. For high damping situation, the energy loss equation is derived by considering the relationship between potential energy and total energy. Then, the energy density governing equation is obtained. Finally, the feasibility of the EFA approach is validated by comparing the EFA results with the modal solutions for various frequencies and structural damping loss factors. The effects of structural damping loss factor and axial force on the energy density distribution are also discussed in detail.New analytical free vibration solutions of orthotropic rectangular thin plates using generalized integral transformation.https://zbmath.org/1459.740812021-05-28T16:06:00+00:00"Zhang, Jinghui"https://zbmath.org/authors/?q=ai:zhang.jinghui"Ullah, Salamat"https://zbmath.org/authors/?q=ai:ullah.salamat"Zhong, Yang"https://zbmath.org/authors/?q=ai:zhong.yangSummary: A first endeavor is made to obtain the analytical free vibration solutions of orthotropic rectangular thin plates utilizing the generalized integral transformation technique. Owing to the nature of the problem, it is very hard to get the exact solution of the title problem by common inverse/semi-inverse method. In solution procedure, the vibrating beam function is selected as the integral core to form the generalized integral transformation pair. Then, the high order partial differential equation under specific boundary conditions is converted to linear algebraic equations and the exact solution is achieved in a straightforward way. One of the advantages of the proposed method is its simplicity and versatility and does not require pre-determining the deflection function which makes the solving procedure more reasonable. The method has wide applications range and can handle other elastic plate problems, such as shear buckling, buckling, and bending. The present results are validated by comparing with the existing analytical solutions which show satisfactory agreement.Free vibration and static bending analysis of piezoelectric functionally graded material plates resting on one area of two-parameter elastic foundation.https://zbmath.org/1459.740672021-05-28T16:06:00+00:00"Hong Nguyen Thi"https://zbmath.org/authors/?q=ai:hong-nguyen-thi.Summary: Free vibration and static bending analysis of piezoelectric functionally graded material plates resting on one area of the two-parameter elastic foundation is firstly investigated in this paper. The third-order shear deformation theory of Reddy and 8-node plate elements are employed to derive the finite element formulations of the structures; this theory does not need any shear correction factors; however, the mechanical response of the structure is described exactly. Verification problems are performed to evaluate the accuracy of the proposed theory and mathematical model. A wide range of parameter study is investigated to figure out the effect of geometrical, physical, and material properties such as the plate dimension, volume fraction index, piezoelectric effect, elastic foundation coefficients, and the square size of the area of the foundation on the free vibration and static bending of piezoelectric functionally graded material plates. These numerical results of this work aim to contribute to scientific knowledge of these smart structures in engineering practice.Comparison of two models for human-structure interaction.https://zbmath.org/1459.920172021-05-28T16:06:00+00:00"Zhou, Ding"https://zbmath.org/authors/?q=ai:zhou.ding"Han, Huixuan"https://zbmath.org/authors/?q=ai:han.huixuan"Ji, Tianjian"https://zbmath.org/authors/?q=ai:ji.tianjian"Xu, Xiuli"https://zbmath.org/authors/?q=ai:xu.xiuliSummary: This paper studies the vibratory characteristics of human-structure interaction. The two-degree-of-freedom (TDOF) system is developed to describe the coupled vibration of the body and the structure, in which one degree is from the structure and the other degree from the body. Two kinds of modelling methods are used to develop the TDOF system, respectively. One method is called as the separative modelling, which firstly models the structure and the body separately to be independent single-degree-of-freedom (SDOF) systems and then physically combines the two SDOF systems to form a TDOF system. The other method is called as the integrative modelling, which considers the body and the structure as an inseparable whole to develop the coupled TDOF system. It is shown that the present integrative modelling method is more reasonable than the conventional separative modelling method. The differences between two kinds of models are checked in detail when the human body is considered as a two-segment elastic bar with four kinds of typical mass and stiffness distributions.Analysis of rotary vibration of rigid friction pipe pile in unsaturated soil.https://zbmath.org/1459.740822021-05-28T16:06:00+00:00"Zhao, Fu-yao"https://zbmath.org/authors/?q=ai:zhao.fu-yao"Xiang, Peng"https://zbmath.org/authors/?q=ai:xiang.pengSummary: Based on the mixture theory and previous work, the governing equation of the rotary vibration of rigid friction pipe pile in unsaturated soil is established. The analytical solution of this equation can be used to analyze the displacements and the complex stiffness of rotary vibration. The results show that the contribution to stiffness is as follows: solid < liquid < gas; and the contribution to rotational impedance is as follows: solid > liquid > gas. In addition, when the fluid permeability coefficient decreases, the stiffness decreases and the rotational impedance increases, but the influence is not obvious (especially the gas permeability coefficient). Four different kinds of degradation problems are also presented. Relevant conclusions can provide reference for engineering application.Green's function for frequency analysis of thin annular plates with nonlinear variable thickness.https://zbmath.org/1459.741172021-05-28T16:06:00+00:00"Zur, Krzysztof Kamil"https://zbmath.org/authors/?q=ai:zur.krzysztof-kamilSummary: This study considers the free vibration analysis of homogeneous and isotropic annular thin plates with variable distributions of parameters by using the properties of Green's function and Neumann series. The general forms of Green's function depending on the Poisson ratio and the coefficient of distribution for the plate's flexural rigidity and thickness are obtained in closed-form. The fundamental solutions of differential Euler equations are expanded in the Neumann power series using the method of successive approximation based on the properties of integral equations. This approach allows us to obtain the nonlinear frequency equations as a power series that converges rapidly to exact eigenvalues for different power index values and Poisson ratio values. The Neumann power series can then be used to solve the boundary value problem for the free vibration of circular and annular plates with discrete elements, such as an additional mass or ring elastic support. Numerical solutions of the characteristic equations are presented for annular plates with constant and hyperbolic varying thickness, as well as different boundary conditions. The results obtained are compared with selected results from previous studies.Eigenoscillations and stability of orthotropic shells, close to cylindrical ones, with an elastic filler and under the action of meridional forces, normal pressure and temperature.https://zbmath.org/1459.741192021-05-28T16:06:00+00:00"Kukudzhanov, S."https://zbmath.org/authors/?q=ai:kukudzhanov.sergo|kukudzhanov.s-nFree vibrations and stability of closed orthotropic shells, closed by their form to cylindrical ones, with a filler and with applied meridional forces, external pressure and temperature are investigated. The shells are thin and elastic. The temperature is uniformly distributed; an extension of a filler by heating is not taken into account. The shells of positive and negative Gaussian curvatures are investigated. The dependence of the first frequency of free vibrations on orthotropy parameters, meridional loading, external pressure, temperature, and on rigidity of filler ise obtained. It is found that the elastic orthotropy parameters affect significantly the first frequency. Critical values of different effects are determined.
Reviewer: V. Leontiev (Ul'yanovsk)A discrete nonlinear tracking-differentiator and its application in vibration suppression of Maglev system.https://zbmath.org/1459.930462021-05-28T16:06:00+00:00"Wang, Zhiqiang"https://zbmath.org/authors/?q=ai:wang.zhi-qiang|wang.zhiqiang"Long, Zhiqiang"https://zbmath.org/authors/?q=ai:long.zhiqiang"Xie, Yunde"https://zbmath.org/authors/?q=ai:xie.yunde"Ding, Jingfang"https://zbmath.org/authors/?q=ai:ding.jingfang"Luo, Jie"https://zbmath.org/authors/?q=ai:luo.jie"Li, Xiaolong"https://zbmath.org/authors/?q=ai:li.xiaolongSummary: Vibration of the maglev train levitation system is harmful to riding comfort and safety. The signal processing method is effective in vibration control. In this paper, a novel kind of second-order nonlinear tracking differentiator is proposed and applied to suppress the vibration phenomenon. The switching curves of the second-order discrete time optimal control system are presented by the isochronous region method. A synthetic function is acquired depending on the cases whether a point in the phase plane can reach the switching curves within one sample step. The discrete form of tracking differentiator is constructed based on the position relationship between the state point and the characteristic curves. Numerical simulation shows that this discrete tracking differentiator can quickly track an input signal without overshoot and chattering and can produce a good differential signal. A test in a maglev test bench also demonstrates the effectiveness of the tracking differentiator in the suppression of the track-train vibration.Reduced basis isogeometric mortar approximations for eigenvalue problems in vibroacoustics.https://zbmath.org/1459.741852021-05-28T16:06:00+00:00"Horger, Thomas"https://zbmath.org/authors/?q=ai:horger.thomas"Wohlmuth, Barbara"https://zbmath.org/authors/?q=ai:wohlmuth.barbara-i"Wunderlich, Linus"https://zbmath.org/authors/?q=ai:wunderlich.linusSummary: We simulate the vibration of a violin bridge in a multi-query context using reduced basis techniques. The mathematical model is based on an eigenvalue problem for the orthotropic linear elasticity equation. In addition to the nine material parameters, a geometrical thickness parameter is considered. This parameter enters as a 10th material parameter into the system by a mapping onto a parameter independent reference domain. The detailed simulation is carried out by isogeometric mortar methods. Weakly coupled patch-wise tensorial structured isogeometric elements are of special interest for complex geometries with piecewise smooth but curvilinear boundaries. To obtain locality in the detailed system, we use the saddle point approach and do not apply static condensation techniques. However within the reduced basis context, it is natural to eliminate the Lagrange multiplier and formulate a reduced eigenvalue problem for a symmetric positive definite matrix. The selection of the snapshots is
controlled by a multi-query greedy strategy taking into account an error indicator allowing for multiple eigenvalues.
For the entire collection see [Zbl 1381.65001].Influence of oscillation localization on film detachment from a substrate.https://zbmath.org/1459.740132021-05-28T16:06:00+00:00"Abramyan, A. K."https://zbmath.org/authors/?q=ai:abramyan.a-k"Bessonov, N. M."https://zbmath.org/authors/?q=ai:bessonov.nicholas-m"Indeitsev, D. A."https://zbmath.org/authors/?q=ai:indeitsev.dmitrii-anatolevich"Mochalova, Yu. A."https://zbmath.org/authors/?q=ai:mochalova.yuliya-alekseevna"Semenov, B. N."https://zbmath.org/authors/?q=ai:semenov.b-nSummary: In modern constructions, thin-layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical-mechanical properties, which leads to the destruction or detachment of the cover. Of special interest is strength analysis under dynamical or vibrational impacts because of the possibility of localizing oscillations in a neighborhood of the initial inhomogeneities (such as inclusions, defects, construction elements, etc.).
In this paper, on the example of the detachment of a string from an elastic substrate, the possibility of localizing oscillations on a detachment defect is demonstrated and the effect of this localization on the growth of the detachment zone is analyzed. A simplified setting of the problem is considered. The possibility of localizing oscillations on a detachment defect is demonstrated and an approximate analytical solution is constructed, which takes into account only the first symmetric form of oscillations describing the development of the initial detachment.
A numerical modeling of the problem is performed, and the results of modeling are compared with the approximate analytical solution.A modified incremental harmonic balance method for 2-DOF airfoil aeroelastic systems with nonsmooth structural nonlinearities.https://zbmath.org/1459.700082021-05-28T16:06:00+00:00"Ni, Ying-Ge"https://zbmath.org/authors/?q=ai:ni.yingge"Zhang, Wei"https://zbmath.org/authors/?q=ai:zhang.wei.19"Lv, Yi"https://zbmath.org/authors/?q=ai:lv.yiSummary: A modified incremental harmonic balance method is presented to analyze the aeroelastic responses of a 2-DOF airfoil aeroelastic system with a nonsmooth structural nonlinearity. The current method, which combines the traditional incremental harmonic balance method and a fast Fourier transform, can be used to obtain the higher-order approximate solution for the aeroelastic responses of a 2-DOF airfoil aeroelastic system with a nonsmooth structural nonlinearity using significantly fewer linearized algebraic equations than the traditional method, and the dominant frequency components of the response can be obtained by a fast Fourier transform of the numerical solution. Thus, periodic solutions can be obtained, and the calculation process can be simplified. Furthermore, the nonsmooth nonlinearity was expanded into a Fourier series. The procedures of the modified incremental harmonic balance method were demonstrated using systems with hysteresis and free play nonlinearities. The modified incremental harmonic balance method was validated by comparing with the numerical solutions. The effect of the number of harmonics on the solution precision as well as the effect of the free-play and stiffness ratio on the response amplitude is discussed.A new analytical method for spherical thin shells' axisymmetric vibrations.https://zbmath.org/1459.740712021-05-28T16:06:00+00:00"Nassit, Mariame"https://zbmath.org/authors/?q=ai:nassit.mariame"El Harif, Abderrahmane"https://zbmath.org/authors/?q=ai:el-harif.abderrahmane"Berbia, Hassan"https://zbmath.org/authors/?q=ai:berbia.hassan"Taha Janan, Mourad"https://zbmath.org/authors/?q=ai:taha-janan.mouradSummary: In order to improve the spherical thin shells' vibrations analysis, we introduce a new analytical method. In this method, we take into consideration the terms of the inertial couples in the stress couples' differential equations of motion. These inertial couples are omitted in the theories provided by Naghdi-Kalnins and Kunieda. The results show that the current method can solve the axisymmetric vibrations' equations of elastic thin spherical shells. In this paper, we focus on verifying the current method, particularly for free vibrations with free edge and clamped edge boundary conditions. To check the validity and accuracy of the current analytical method, the natural frequencies determined by this method are compared with those available in the literature and those obtained by a finite element calculation.Forced vibration in cutting process considering the nonlinear curvature and inertia of a rotating composite cutter bar.https://zbmath.org/1459.740772021-05-28T16:06:00+00:00"Ren, Yongsheng"https://zbmath.org/authors/?q=ai:ren.yongsheng"Yao, Donghui"https://zbmath.org/authors/?q=ai:yao.donghuiSummary: Forced vibration of the cutting system with a three-dimensional composite cutter bar is investigated. The composite cutter bar is simplified as a rotating cantilever shaft which is subjected to a cutting force including regenerative delay effects and harmonic exciting items. The nonlinear curvature and inertia of the cutter bar are taken into account based on inextensible assumption. The effects of the moment of inertia, gyroscopic effect, and internal and external damping are also considered, but shear deformation is neglected. Equation of motion is derived based on Hamilton's extended principle and discretized by the Galerkin method. The analytical solutions of the steady-state response of the cutting system are constructed by using the method of multiple scales. The response of the cutting system is studied for primary and superharmonic resonances. The effects of length-to-diameter ratio, damping ratio, cutting force coefficients, ply angle, rotating speed, and internal and external damping are investigated. The results show that nonlinear curvature and inertia imposed a significant effect on the dynamic behavior of the cutting process. The equivalent nonlinearity of the cutting system shows hard spring characteristics. Multiple solutions and jumping phenomenon of typical Duffing system are found in forced response curves.Application of differential cubature method for nonlocal vibration, buckling and bending response of annular nanoplates integrated by piezoelectric layers based on surface-higher order nonlocal-piezoelasticity theory.https://zbmath.org/1459.740702021-05-28T16:06:00+00:00"Motezaker, Mohsen"https://zbmath.org/authors/?q=ai:motezaker.mohsen"Jamali, Majid"https://zbmath.org/authors/?q=ai:jamali.majid"Kolahchi, Reza"https://zbmath.org/authors/?q=ai:kolahchi.rezaSummary: This paper deals with the vibration, buckling and bending analyses of annular nanoplate integrated with piezoelectric layers at the top and bottom surfaces. The higher order nonlocal theory for size effect and Gurtin-Murdoch theory for surface effects are utilized. The governing equations are derived based on the layer-wise (LW) theory and Hamilton's principle. The differential cubature method (DCM) as a new numerical procedure is utilized to solve the motion equations for obtaining the frequency, buckling load and deflection. The influences of various parameters such as external voltage, boundary condition, surface stresses, nonlocal parameter, outer to inner radius ratio and core to top layer thickness ratio were shown on the vibration, buckling and bending responses of the nanostructure. The results of vibration, buckling and bending are validated with other published works. The outcomes show that the surface stresses have a significant effect on the increases of the frequency and buckling load and decrease of the deflection.Vibration and stability analysis of functionally graded skew plate using higher order shear deformation theory.https://zbmath.org/1459.740742021-05-28T16:06:00+00:00"Parida, S."https://zbmath.org/authors/?q=ai:parida.sailitniyazi|parida.suvendu|parida.s-k"Mohanty, S. C."https://zbmath.org/authors/?q=ai:mohanty.sukesh-chandraSummary: This paper deals with the vibration and buckling analysis of skew functionally graded material (FGM) plates. A finite element mathematical model is developed based on higher order shear deformation theory. The model is based on an eight noded isoparametric element with seven degrees of freedom per node. The material properties are graded along thickness direction obeying simple power-law distribution. The general displacement equation provides \(\mathrm{C}^{0}\) continuity. The transverse shear strain undergoes parabolic variation through the thickness of the plate. Hence, there is no requirement of a shear correction factor in this theory. The governing equation for the skew FGM plate is obtained using Hamilton's principle. The obtained results are compared with the published results to determine the accuracy of the method. The effect of various parameters like aspect ratio, side-thickness ratio, volume fraction index, boundary conditions and skew angle on the natural frequencies and buckling loads has been investigated.Trapped modes due to narrow cracks in thin simply-supported elastic plates.https://zbmath.org/1459.740972021-05-28T16:06:00+00:00"Porter, R."https://zbmath.org/authors/?q=ai:porter.richard-d"Evans, D. V."https://zbmath.org/authors/?q=ai:evans.david-vSummary: We consider an elastic plate of infinite length and constant width supported simply along its two parallel edges and having a finite length crack along its centreline. In particular, we look for and find trapped modes (localised oscillations) in the presence of the crack. An explicit wide-spacing approximation based on the Wiener-Hopf technique applied to incident wave scattering by semi-infinite cracks is complemented by an exact formulation of the problem in the form of integro-differential equations. An application of a Galerkin method for the numerical calculation of results from the latter method leads to a novel explicit 'small-spacing' approximation. In combination with the wide-spacing results this is shown to provide accurate results for all lengths of crack.Fractional-order models for the static and dynamic analysis of nonlocal plates.https://zbmath.org/1459.741122021-05-28T16:06:00+00:00"Patnaik, Sansit"https://zbmath.org/authors/?q=ai:patnaik.sansit"Sidhardh, Sai"https://zbmath.org/authors/?q=ai:sidhardh.sai"Semperlotti, Fabio"https://zbmath.org/authors/?q=ai:semperlotti.fabioSummary: This study presents the analytical formulation and the finite element solution of a fractional-order nonlocal plate under both Mindlin and Kirchhoff formulations. By employing consistent definitions for fractional-order kinematic relations, the governing equations and the associated boundary conditions are derived based on variational principles. Remarkably, the fractional-order nonlocal model gives rise to a self-adjoint and positive-definite system that accepts a unique solution. Further, owing to the difficulty in obtaining analytical solutions to this fractional-order differ-integral problem, a 2D finite element model for the fractional-order governing equations is presented. Following a thorough validation against benchmark problems, the 2D fractional finite element model is used to study the static as well as the free dynamic response of fractional-order plates subject to various loading and boundary conditions. It is established that the fractional-order nonlocality leads to a reduction in the stiffness of the plate structure thereby increasing the displacements and reducing the natural frequency of vibration of the plates. Further, it is seen that the effect of nonlocality is stronger on the higher modes of vibration when compared to the fundamental mode. These effects of the fractional-order nonlocality are observed irrespective of the nature of the boundary conditions. More specifically, the fractional-order model of nonlocal plates is free from boundary effects that lead to mathematical ill-posedness and inaccurate (paradoxical) predictions such as hardening and absence of nonlocal effects, typical of classical strain-driven integral approaches to nonlocal elasticity. This consistency in the predictions is a result of the well-posed nature of the fractional-order governing equations that accept a unique solution.A modified dual-level algorithm for large-scale three-dimensional Laplace and Helmholtz equation.https://zbmath.org/1459.652292021-05-28T16:06:00+00:00"Li, Junpu"https://zbmath.org/authors/?q=ai:li.junpu"Chen, Wen"https://zbmath.org/authors/?q=ai:chen.wen|chen.wen.1"Fu, Zhuojia"https://zbmath.org/authors/?q=ai:fu.zhuojiaSummary: A modified dual-level algorithm is proposed in the article. By the help of the dual level structure, the fully-populated interpolation matrix on the fine level is transformed to a local supported sparse matrix to solve the highly ill-conditioning and excessive storage requirement resulting from fully-populated interpolation matrix. The kernel-independent fast multipole method is adopted to expediting the solving process of the linear equations on the coarse level. Numerical experiments up to 2-million fine-level nodes have successfully been achieved. It is noted that the proposed algorithm merely needs to place 2-3 coarse-level nodes in each wavelength per direction to obtain the reasonable solution, which almost down to the minimum requirement allowed by the Shannon's sampling theorem. In the real human head model example, it is observed that the proposed algorithm can simulate well computationally very challenging exterior high-frequency harmonic acoustic wave propagation up to 20,000 Hz.Cauchy problem for the torsional vibration equation of a nonlinear-elastic rod of infinite length.https://zbmath.org/1459.740802021-05-28T16:06:00+00:00"Umarov, Kh. G."https://zbmath.org/authors/?q=ai:umarov.khasan-galsanovichThe author studies the solvability of the problem of torsional vibrations of an infinite nonlinear-elastic rod in the space of continuous functions. This is generally modeled by a Sobolev-type equation that is not resolved with respect to the time derivative of the second order
\[
Du = \beta\frac{\partial}{\partial x}\Big(\frac{\partial u}{\partial x}\Big)^3,\qquad D=\frac{\partial^2}{\partial t^2} -\frac{\partial^4}{\partial x^2\partial t^2} -\frac{\partial^2}{\partial x^2}+\alpha^2 \frac{\partial^4}{\partial x^4},
\]
which, after a suitable change of variable, becomes
\[
\frac{\partial^2 \theta }{\partial t^2} - c_1^2 \frac{\partial^2\theta}{\partial x^2} -\frac{I_\varphi}{I_0} \frac{\partial^2}{\partial x^2}\Big(\frac{\partial^2 \theta}{\partial t^2} -c_0^2 \frac{\partial^2\theta}{\partial x^2}\Big)=0.
\]
A Cauchy problem associated to this equation then requires imposing initial conditions
\[
u(x,0)=\varphi(x),\qquad u_t(x,0)=\psi(x).
\]
In the first part, the author proves that, when the initial conditions and their derivatives up to the fourth order are continuous, then the Cauchy problem is well posed, at least locally in time, and admits a solution in the strong sense.
Then, the author shows also uniqueness of the strong solution, and provides some quantitative estimates on the regularity of such solutions.
The second part is devoted to the global-in-time well-posedness of the Cauchy problem: the author shows that, when the initial data
\[
\varphi \in W^{1,4}(\mathbb{R})\cap H^2(\mathbb{R}),\qquad \psi \in W^{1,2}(\mathbb{R}),
\]
then the strong solution belongs to \(W^{1,2}(\mathbb{R})\), is globally well defined in time, and its \(C^0\) norm grows at most exponentially in time. On the other hand, if the initial data satisfies
\[
\|\varphi\|_{W^{1,2}(\mathbb{R})}^2>0,\qquad M:= \langle \varphi,\psi \rangle+\langle \varphi',\psi' \rangle>0,\qquad Z_0< M^2 \|\varphi\|_{W^{1,2}(\mathbb{R})}^{-2},
\]
then no global-in-time solution can exist, and the author estimates the maximum blow-up time.
Reviewer: Xin Yang Lu (Thunder Bay)An ES-MITC3 finite element method based on higher-order shear deformation theory for static and free vibration analyses of FG porous plates reinforced by GPLs.https://zbmath.org/1459.740792021-05-28T16:06:00+00:00"Tran, The-Van"https://zbmath.org/authors/?q=ai:tran.the-van"Tran, Tuan-Duy"https://zbmath.org/authors/?q=ai:tran.tuan-duy"Hoa Pham, Quoc"https://zbmath.org/authors/?q=ai:pham.quoc-hoa"Nguyen-Thoi, Trung"https://zbmath.org/authors/?q=ai:nguyen-thoi.trung"Tran, Van Ke"https://zbmath.org/authors/?q=ai:tran.van-keSummary: An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique (MITC) for triangular elements, named as ES-MITC3, was recently proposed to enhance the accuracy of the original MITC3 for analysis of plates and shells. In this study, the ES-MITC3 is extended to the static and vibration analysis of functionally graded (FG) porous plates reinforced by graphene platelets (GPLs). In the ES-MITC3, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains created by two adjacent triangular elements sharing an edge. The effective material properties are variable through the thickness of plates including Young's modulus estimated via the Halpin-Tsai model and Poisson's ratio and the mass density according to the rule of mixture. Three types of porosity distributions and GPL dispersion pattern into the metal matrix are examined. Numerical examples are given to demonstrate the performance of the present approach in comparison with other existing methods. Furthermore, the effect of several parameters such as GPL weight fraction, porosity coefficient, porosity distribution, and GPL dispersion patterns on the static and free vibration responses of FG porous plates is discussed in detail.An improved analytical method for vibration analysis of variable section beam.https://zbmath.org/1459.740662021-05-28T16:06:00+00:00"Feng, Jingjing"https://zbmath.org/authors/?q=ai:feng.jingjing"Chen, Zhengneng"https://zbmath.org/authors/?q=ai:chen.zhengneng"Hao, Shuying"https://zbmath.org/authors/?q=ai:hao.shuying"Zhang, Kunpeng"https://zbmath.org/authors/?q=ai:zhang.kunpengSummary: The variable section structure could be the physical model of many vibration problems, and its analysis becomes more complicated either. It is very important to know how to obtain the exact solution of the modal function and the natural frequency effectively. In this paper, a general analytical method, based on segmentation view and iteration calculation, is proposed to obtain the modal function and natural frequency of the beam with an arbitrary variable section. In the calculation, the section function of the beam is considered as an arbitrary function directly, and then the result is obtained by the proposed method that could have high precision. In addition, the total amount of calculation caused by high-order Taylor expansion is reduced greatly by comparing with the original Adomian decomposition method (ADM). Several examples of the typical beam with different variable sections are calculated to show the excellent calculation accuracy and convergence of the proposed method. The correctness and effectiveness of the proposed method are verified also by comparing the results of the several kinds of the theoretical method, finite element simulation, and experimental method.Thermoelastic vibrations of a Timoshenko microbeam based on the modified couple stress theory.https://zbmath.org/1459.740092021-05-28T16:06:00+00:00"Awrejcewicz, J."https://zbmath.org/authors/?q=ai:awrejcewicz.jan"Krysko, V. A."https://zbmath.org/authors/?q=ai:krysko.vadim-a|krysko.vadim-a-jun"Pavlov, S. P."https://zbmath.org/authors/?q=ai:pavlov.s-p"Zhigalov, M. V."https://zbmath.org/authors/?q=ai:zhigalov.maxim-v"Kalutsky, L. A."https://zbmath.org/authors/?q=ai:kalutsky.l-a"Krysko, A. V."https://zbmath.org/authors/?q=ai:krysko.anton-vSummary: The dependence of the quality factor of nonlinear microbeam resonators under thermoelastic damping for Timoshenko beams with regard to geometric nonlinearity has been studied. The constructed mathematical model is based on the modified couple stress theory which implies prediction of size-dependent effects in microbeam resonators. The Hamilton principle has yielded coupled nonlinear thermoelastic PDEs governing dynamics of the Timoshenko microbeams for both plane stresses and plane deformations. Nonlinear thermoelastic vibrations are studied analytically and numerically and quality factors of the resonators versus geometric and material microbeam properties are estimated. Results are presented for gold microbeams for different ambient temperatures and different beam thicknesses, and they are compared with results yielded by the classical theory of elasticity in linear/nonlinear cases.