×

A nonlinear surface-stress-dependent model for vibration analysis of cylindrical nanoscale shells conveying fluid. (English) Zbl 1480.74131

Summary: A nonlinear surface-stress-dependent nanoscale shell model is developed on the base of the classical shell theory incorporating the surface stress elasticity. Nonlinear free vibrations of circular cylindrical nanoshells conveying fluid are studied in the framework of the proposed model. In order to describe the large-amplitude motion, the von Kármán nonlinear geometrical relations are taken into account. The governing equations are derived by using Hamilton’s principle. Then, the method of multiple scales is adopted to perform an approximately analytical analysis on the present problem. Results show that the surface stress can influence the vibration characteristics of fluid-conveying thin-walled nanoshells. This influence becomes more and more considerable with the decrease of the wall thickness of the nanoshells. Furthermore, the fluid speed, the fluid mass density, the initial surface tension and the nanoshell geometry play important roles on the nonlinear vibration characteristics of fluid-conveying nanoshells.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74K25 Shells
76A20 Thin fluid films
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lam, D. C.C.; Yang, F.; Chong, A. C.M.; Wang, J.; Tong, P., Experiments and theory in strain gradient elasticity, J. Mech. Phys. Solids, 51, 1477-1508 (2003) · Zbl 1077.74517
[2] Lei, J.; He, Y.; Guo, S.; Li, Z.; Liu, D., Size-dependent vibration of nickel cantilever microbeams: experiment and gradient elasticity, AIP Adv., 6, Article 105202 pp. (2016)
[3] Liu, D.; He, Y.; Dunstan, D. J.; Zhang, B.; Gan, Z.; Hu, P.; Ding, H., Toward a further understanding of size effects in the torsion of thin metal wires: An experimental and theoretical assessment, Int. J. Plast., 41, 30-52 (2013)
[4] Eringen, A. C.; Edelen, D., On nonlocal elasticity, Int. J. Eng. Sci., 10, 233-248 (1972) · Zbl 0247.73005
[5] Eringen, A. C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., 54, 4703-4710 (1983)
[6] Mindlin, R. D., Second gradient of strain and surface-tension in linear elasticity, Int. J. Solids Struct., 1, 417-438 (1965)
[7] Mindlin, R. D.; Tiersten, H. F., Effects of couple-stresses in linear elasticity, Arch. Ration. Mech. Anal., 11, 415-448 (1962) · Zbl 0112.38906
[8] Yang, F.; Chong, A. C.M.; Lam, D. C.C.; Tong, P., Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct., 39, 2731-2743 (2002) · Zbl 1037.74006
[9] Gurtin, M. E.; Murdoch, A. I., A continuum theory of elastic material surfaces, Arch. Ration. Mech. Anal., 57, 291-323 (1975) · Zbl 0326.73001
[10] Gurtin, M. E.; Murdoch, A. I., Surface stress in solids, Int. J. Solids Struct., 14, 431-440 (1978) · Zbl 0377.73001
[11] Gibbs, J. W., The Scientific Papers of J. Willard Gibbs (1906), Green and Company: Green and Company Longmans · JFM 37.0035.06
[12] Ru, C. Q., A strain-consistent elastic plate model with surface elasticity, Continuum Mech. Thermodyn., 28, 263-273 (2016) · Zbl 1348.74217
[13] Yue, Y. M.; Ru, C. Q.; Xu, K. Y., Modified von Kármán equations for elastic nanoplates with surface tension and surface elasticity, Int. J. Non-Linear Mech., 88, 67-73 (2017)
[14] Rouhi, H.; Ansari, R.; Darvizeh, M., Nonlinear free vibration analysis of cylindrical nanoshells based on the Ru model accounting for surface stress effect, Int. J. Mech. Sci., 113, 1-9 (2016)
[15] Shenoy, V. B., Atomistic calculations of elastic properties of metallic fcc crystal surfaces, Phys. Rev. B, 71, Article 094104 pp. (2005)
[16] Miller, R. E.; Shenoy, V. B., Size-dependent elastic properties of nanosized structural elements, Nanotechnology, 11, 139 (2000)
[17] Karniadakis, G.; Beskok, A.; Aluru, N., Microflows and Nanoflows: Fundamentals and Simulation (2006), Springer Science & Business Media
[18] Mirramezani, M.; Mirdamadi, H. R.; Ghayour, M., Nonlocal vibrations of shell-type CNT conveying simultaneous internal and external flows by considering slip condition, Comput. Methods Appl. Mech. Eng., 272, 100-120 (2014) · Zbl 1296.74026
[19] Rashidi, V.; Mirdamadi, H. R.; Shirani, E., A novel model for vibrations of nanotubes conveying nanoflow, Comput. Mater. Sci., 51, 347-352 (2012)
[20] Ke, L.-L.; Wang, Y.-S., Flow-induced vibration and instability of embedded double-walled carbon nanotubes based on a modified couple stress theory, Phys. E: Low-Dimens. Syst. Nanostruct., 43, 1031-1039 (2011)
[21] Wang, L.; Liu, H. T.; Ni, Q.; Wu, Y., Flexural vibrations of microscale pipes conveying fluid by considering the size effects of micro-flow and micro-structure, Int. J. Eng. Sci., 71, 92-101 (2013) · Zbl 1423.74288
[22] Deng, J.; Liu, Y.; Liu, W., Size-dependent vibration analysis of multi-span functionally graded material micropipes conveying fluid using a hybrid method, Microfluidics Nanofluidics, 21, 133 (2017)
[23] Li, L.; Hu, Y.; Li, X.; Ling, L., Size-dependent effects on critical flow velocity of fluid-conveying microtubes via nonlocal strain gradient theory, Microfluidics Nanofluidics, 20, 76 (2016)
[24] Zeighampour, H.; Tadi Beni, Y., Size-dependent vibration of fluid-conveying double-walled carbon nanotubes using couple stress shell theory, Phys. E: Low-Dimens. Syst. Nanostruct., 61, 28-39 (2014)
[25] Wang, L., Size-dependent vibration characteristics of fluid-conveying microtubes, J. Fluids Struct., 26, 675-684 (2010)
[26] Hosseini, M.; Bahaadini, R., Size dependent stability analysis of cantilever micro-pipes conveying fluid based on modified strain gradient theory, Int. J. Eng. Sci., 101, 1-13 (2016)
[27] Zhang, J.; Meguid, S. A., Effect of surface energy on the dynamic response and instability of fluid-conveying nanobeams, Eur. J. Mech. - A/Solids, 58, 1-9 (2016) · Zbl 1406.74417
[28] Mohammadimehr, M.; Mehrabi, M., Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow, Appl. Math. Model., 47, 685-709 (2017) · Zbl 1446.74038
[29] Zeighampour, H.; Beni, Y. T.; Karimipour, I., Wave propagation in double-walled carbon nanotube conveying fluid considering slip boundary condition and shell model based on nonlocal strain gradient theory, Microfluidics Nanofluidics, 21, 85 (2017)
[30] Ansari, R.; Gholami, R.; Norouzzadeh, A.; Sahmani, S., Size-dependent vibration and instability of fluid-conveying functionally graded microshells based on the modified couple stress theory, Microfluidics Nanofluidics, 19, 509-522 (2015)
[31] Ansari, R.; Gholami, R.; Norouzzadeh, A.; Darabi, M. A., Surface stress effect on the vibration and instability of nanoscale pipes conveying fluid based on a size-dependent Timoshenko beam model, Acta Mech. Sin., 31, 708-719 (2015) · Zbl 1345.74034
[32] Ghazavi, M. R.; Molki, H.; Ali beigloo, A., Nonlinear vibration and stability analysis of the curved microtube conveying fluid as a model of the micro coriolis flowmeters based on strain gradient theory, Appl. Math. Model., 45, 1020-1030 (2017) · Zbl 1446.74016
[33] Yang, T.-Z.; Ji, S.; Yang, X.-D.; Fang, B., Microfluid-induced nonlinear free vibration of microtubes, Int. J. Eng. Sci., 76, 47-55 (2014)
[34] Hu, W.; Deng, Z., Chaos in embedded fluid-conveying single-walled carbon nanotube under transverse harmonic load series, Nonlinear Dyn., 79, 325-333 (2015)
[35] Dehrouyeh-Semnani, A. M.; Nikkhah-Bahrami, M.; Yazdi, M. R.H., On nonlinear vibrations of micropipes conveying fluid, Int. J. Eng. Sci., 117, 20-33 (2017) · Zbl 1423.74387
[36] Mashrouteh, S.; Sadri, M.; Younesian, D.; Esmailzadeh, E., Nonlinear vibration analysis of fluid-conveying microtubes, Nonlinear Dyn., 85, 1007-1021 (2016)
[37] Setoodeh, A. R.; Afrahim, S., Nonlinear dynamic analysis of FG micro-pipes conveying fluid based on strain gradient theory, Compos. Struct., 116, 128-135 (2014)
[38] Ansari, R.; Norouzzadeh, A.; Gholami, R.; Faghih Shojaei, M.; Hosseinzadeh, M., Size-dependent nonlinear vibration and instability of embedded fluid-conveying SWBNNTs in thermal environment, Phys. E: Low-Dimens. Syst. Nanostruct., 61, 148-157 (2014)
[39] Ghorbanpour Arani, A.; Bagheri, M. R.; Kolahchi, R.; Khoddami Maraghi, Z., Nonlinear vibration and instability of fluid-conveying DWBNNT embedded in a visco-Pasternak medium using modified couple stress theory, J. Mech. Sci. Technol., 27, 2645-2658 (2013)
[40] Kheibari, F.; Beni, Y. T., Size dependent electro-mechanical vibration of single-walled piezoelectric nanotubes using thin shell model, Mater. Des., 114, 572-583 (2017)
[41] Fattahian Dehkordi, S.; Tadi Beni, Y., Electro-mechanical free vibration of single-walled piezoelectric/flexoelectric nano cones using consistent couple stress theory, Int. J. Mech. Sci., 128-129, 125-139 (2017)
[42] Amabili, M.; Pellicano, F.; PaÏdoussis, M. P., Non-linear dynamics and stability of circular cylindrical shells containing flowing fluid. Part I: stability, J. Sound Vib., 225, 655-699 (1999)
[43] Amabili, M., Nonlinear Vibrations and Stability of Shells and Plates (2008), Cambridge University Press: Cambridge University Press New York · Zbl 1154.74002
[44] Wang, Y. Q.; Liang, L.; Guo, X. H., Internal resonance of axially moving laminated circular cylindrical shells, J. Sound Vib., 332, 6434-6450 (2013)
[45] Wang, Y. Q.; Zu, J. W., Nonlinear dynamics of a translational FGM plate with strong mode interaction, Int. J. Struct. Stab. Dyn., 18, Article 1850031 pp. (2018)
[46] Wang, Y. Q., Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state, Acta Astronaut., 143, 263-271 (2018)
[47] Wang, Y. Q.; Zu, J. W., Nonlinear steady-state responses of longitudinally traveling functionally graded material plates in contact with liquid, Compos. Struct., 164, 130-144 (2017)
[48] Nayfeh, A. H.; Mook, D. T., Nonlinear Oscillations (2008), Wiley-VCH
[49] Zhang, W.; Liu, T.; Xi, A.; Wang, Y. N., Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes, J. Sound Vib., 423, 65-99 (2018)
[50] Rouhi, H.; Ansari, R.; Darvizeh, M., Analytical treatment of the nonlinear free vibration of cylindrical nanoshells based on a first-order shear deformable continuum model including surface influences, Acta Mech., 227, 1767-1781 (2016) · Zbl 1341.74131
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.