Articles

Nonlinear dynamic responses of sandwich functionally graded porous cylindrical shells embedded in elastic media under 1:1 internal resonance

Expand
  • State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China

Received date: 2021-01-17

  Revised date: 2021-03-18

  Online published: 2021-05-21

Supported by

the National Natural Science Foundation of China (No. 11972204)

Abstract

In this article, the nonlinear dynamic responses of sandwich functionally graded (FG) porous cylindrical shell embedded in elastic media are investigated. The shell studied here consists of three layers, of which the outer and inner skins are made of solid metal, while the core is FG porous metal foam. Partial differential equations are derived by utilizing the improved Donnell's nonlinear shell theory and Hamilton's principle. Afterwards, the Galerkin method is used to transform the governing equations into nonlinear ordinary differential equations, and an approximate analytical solution is obtained by using the multiple scales method. The effects of various system parameters, specifically, the radial load, core thickness, foam type, foam coefficient, structure damping, and Winkler-Pasternak foundation parameters on nonlinear internal resonance of the sandwich FG porous thin shells are evaluated.

Cite this article

Yunfei LIU, Zhaoye QIN, Fulei CHU . Nonlinear dynamic responses of sandwich functionally graded porous cylindrical shells embedded in elastic media under 1:1 internal resonance[J]. Applied Mathematics and Mechanics, 2021 , 42(6) : 805 -818 . DOI: 10.1007/s10483-021-2740-7

References

[1] SPOERKE, E. D., MURRAY, N. G., LI, H., BRINSON, L. C., and STUPP, S. I. A bioactive titanium foam scaffold for bone repair. Acta Biomaterialia, 1, 523-533(2005)
[2] CAO, L., LIN, Y., LU, F., CHEN, R., ZHANG, Z., and LI, Y. Experimental study on the shock absorption performance of combined aluminium honeycombs under impact loading. Shock and Vibration, 2015, 1-8(2015)
[3] LI, M., DENG, Z., LIU, R., and GUO, H. Crashworthiness design optimisation of metal honeycomb energy absorber used in lunar lander. International Journal of Crashworthiness, 16, 411-419(2011)
[4] TAN, W. C., SAW, L. H., XUAN, H. S., CAI, Z., and THIAM,M.C. Overview of porous media/metal foam application in fuel cells and solar power systems. Renewable and Sustainable Energy Reviews, 96, 181-197(2018)
[5] CHOI, K., KIM, J., KO, A., MYUNG, C. L., PARK, S., and LEE, J. Size-resolved engine exhaust aerosol characteristics in a metal foam particulate filter for GDI light-duty vehicle. Journal of Aerosol science, 57, 1-13(2013)
[6] KIM, S. and LEE, C. W. A review on manufacturing and application of open-cell metal foam. Procedia Materials Science, 4, 305-309(2014)
[7] BRESLAVSKY, I. D. and AMABILI, M. Nonlinear vibrations of a circular cylindrical shell with multiple internal resonances under multi-harmonic excitation. Nonlinear Dynamics, 93, 53-62(2018)
[8] YANG, S. W., ZHANG, W., and MAO, J. J. Nonlinear vibrations of carbon fiber reinforced polymer laminated cylindrical shell under non-normal boundary conditions with 1:2 internal resonance. European Journal of Mechanics-A/Solids, 74, 317-336(2019)
[9] ZHANG, Y., LIU, J., and WEN, B. Nonlinear dynamical responses of rotary cylindrical shells with internal resonance. Acta Mechanica Solida Sinica, 32, 186-200(2019)
[10] RODRIGUES, L., SILVA, F. M. A., and GONÇALVES, P. B. Influence of initial geometric imperfections on the 1:1:1:1 internal resonances and nonlinear vibrations of thin-walled cylindrical shells. Thin-Walled Structures, 151, 106730(2020)
[11] LIU, Y., QIN, Z. Y., and CHU, F. L. Analytical study of the impact response of shear deformable sandwich cylindrical shell with a functionally graded porous core. Mechanics of Advanced Materials and Structures, 5, 1-10(2020)
[12] DONG, Y. H., LI, Y. H., CHEN, D., and YANG, J. Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion. Composites Part B:Engineering, 145, 1-13(2018)
[13] LI, Q., DI, W., CHEN, X., LEI, L., YU, Y., and WEI, G. Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler-Pasternak elastic foundation. International Journal of Mechanical Sciences, 148, 596- 610(2018)
[14] CHEN, D., YANG, J., and KITIPORNCHAI, S. Free and forced vibrations of shear deformable functionally graded porous beams. International Journal of Mechanical Sciences, 108-109, 14-22(2016)
[15] GAO, W., QIN, Z., and CHU, F. Wave propagation in functionally graded porous plates reinforced with graphene platelets. Aerospace Science and Technology, 102, 105860(2020)
[16] LIU, Y. F. and WANG, Y. Q. Thermo-electro-mechanical vibrations of porous functionally graded piezoelectric nanoshells. Nanomaterials, 9, 301(2019)
[17] MAGNUCKI, K. and STASIEWICZ, P. Elastic buckling of a porous beam. Journal of Theoretical and Applied Mechanics, 42, 859-868(2004)
[18] MAGNUCKA-BLANDZI, E. Axi-symmetrical deflection and buckling of circular porous-cellular plate. Thin-Walled Structures, 46, 333-337(2008)
[19] JABBARI, M., MOJAHEDIN, A., KHORSHIDVAND, A. R., and ESLAMI, M. R. Buckling analysis of a functionally graded thin circular plate made of saturated porous materials. Journal of Engineering Mechanics, 140, 287-295(2013)
[20] CHEN, D., YANG, J., and KITIPORNCHAI, S. Elastic buckling and static bending of shear deformable functionally graded porous beam. Composite Structures, 133, 54-61(2015)
[21] AMABILI, M. Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, Cambridge (2008)
[22] DING, H., HUANG, L., MAO, X., and CHEN, L. Primary resonance of traveling viscoelastic beam under internal resonance. Applied Mathematics and Mechanics (English Edition), 38, 1-14(2017) https://doi.org/10.1007/s10483-016-2152-6
[23] LI, W., YANG, X. D., ZHANG, W., and REN, Y. Parametric amplification performance analysis of a vibrating beam micro-gyroscope with size-dependent and fringing field effects. Applied Mathematical Modelling, 91, 111-124(2021)
[24] LIU, Y. F., LING, X., and WANG, Y. Q. Free and forced vibration analysis of 3D graphene foam truncated conical microshells. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, 133(2021)
[25] WANG, Y., LIU, Y., and ZU, J. W. Nonlinear free vibration of piezoelectric cylindrical nanoshells. Applied Mathematics and Mechanics (English Edition), 40, 13-32(2019) https://doi.org/10.1007/s10483-019-2476-6
[26] NAYFEH, A. H. and MOOK, D. T. Nonlinear Oscillations, John Wiley & Sons, New Jersey (1995)
[27] ZHANG, W., CHEN, J., ZHANG, Y. F., and YANG, X. D. Continuous model and nonlinear dynamic responses of circular mesh antenna clamped at one side. Engineering Structures, 151, 115-135(2017)
[28] QIN, Z., CHU, F., and ZU, J. Free vibrations of cylindrical shells with arbitrary boundary conditions:a comparison study. International Journal of Mechanical Sciences, 133, 91-99(2017)
[29] DHOOGE, A., GOVAERTS, W., KUZNETSOV, Y. A., MEIJER, H. G. E., and SAUTOIS, B. New features of the software MatCont for bifurcation analysis of dynamical systems. Mathematical and Computer Modelling of Dynamical Systems, 14, 147-175(2008)
Outlines

/

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals