Articles

Nonlinear dynamic analysis of moving bilayer plates resting on elastic foundations

Expand
  • 1. Department of Mechanical Engineering, Mashhad Branch, Azad University, Mashhad 9187144123, Iran;
    2. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad 9177948944, Iran;
    3. Engineering Department, Lancaster University, Bailrigg, Lancaster LA1 4YR, U. K.

Received date: 2019-08-25

  Revised date: 2019-12-07

  Online published: 2020-02-17

Abstract

The aim of this study is to investigate the dynamic response of axially moving two-layer laminated plates on the Winkler and Pasternak foundations. The upper and lower layers are formed from a bidirectional functionally graded (FG) layer and a graphene platelet (GPL) reinforced porous layer, respectively. Henceforth, the combined layers will be referred to as a two-dimensional (2D) FG/GPL plate. Two types of porosity and three graphene dispersion patterns, each of which is distributed through the plate thickness, are investigated. The mechanical properties of the closed-cell layers are used to define the variation of Poisson's ratio and the relationship between the porosity coefficients and the mass density. For the GPL reinforced layer, the effective Young's modulus is derived with the Halpin-Tsai micro-system model, and the rule of mixtures is used to calculate the effective mass density and Poisson's ratio. The material of the upper 2D-FG layer is graded in two directions, and its effective mechanical properties are also derived with the rule of mixtures. The dynamic governing equations are derived with a first-order shear deformation theory (FSDT) and the von Kármán nonlinear theory. A combination of the dynamic relaxation (DR) and Newmark's direct integration methods is used to solve the governing equations in both time and space. A parametric study is carried out to explore the effects of the porosity coefficients, porosity and GPL distributions, material gradients, damping ratios, boundary conditions, and elastic foundation stiffnesses on the plate response. It is shown that both the distributions of the porosity and graphene nanofillers significantly affect the dynamic behaviors of the plates. It is also shown that the reduction in the dynamic deflection of the bilayer composite plates is maximized when the porosity and GPL distributions are symmetric.

Cite this article

M. ESMAEILZADEH, M. KADKHODAYAN, S. MOHAMMADI, G. J. TURVEY . Nonlinear dynamic analysis of moving bilayer plates resting on elastic foundations[J]. Applied Mathematics and Mechanics, 2020 , 41(3) : 439 -458 . DOI: 10.1007/s10483-020-2587-8

References

[1] MEHRABIAN, M. and GOLMAKANI, M. E. Nonlinear bending analysis of radial-stiffened annular laminated sector plates with dynamic relaxation method. Computers and Mathematics with Applications, 69(10), 1272-1302(2015)
[2] NARITA, Y. and TURVEY, G. J. Maximizing the buckling loads of symmetrically laminated composite rectangular plates using a layer wise optimization approach. Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, 218(7), 681-691(2004)
[3] TURVEY, G. J. Large deflection cylindrical bending analysis of cross-ply laminated strips. Journal of Mechanical Engineering Science, 23(1), 21-29(1981)
[4] MOLEIRO, F., MOTA-SOARES, C. M., and CARRERA, E. Three-dimensional exact hygrothermo-elastic solutions for multilayered plates, composite laminates, fiber metal laminates and sandwich plates. Composite Structures, 216, 260-278(2019)
[5] ASHBY, M. F., EVANS, A. G., FLECK, N. A., GIBSON, L. J., HUTCHINSON, J. W., and WADLEY, H. N. G. Metal Foams:A Design Guide, 1st ed., Butterworth-Heinemann, Oxford, 40-54(2000)
[6] SMITH, B. H., SZYNISZEWSKI, S., HAJJAR, J. F., SCHAFER, B. W., and ARWADE, S. R. Steel foam for structures, a review of applications, manufacturing and material properties. Journal of Constructional Steel Research, 71, 1-10(2012)
[7] LEFEBVRE, L. P., BANHART, J., and DUNAND, D. C. Porous metals and metallic foams, current status and recent developments. Advanced Engineering Materials, 10(9), 775-787(2008)
[8] HASSANI, A., HABIBOLAHZADEH, A., and BAFTI, H. Production of graded aluminum foams via powder space holder technique. Materials and Design, 40, 510-515(2012)
[9] GAO, K., LI, R., and YANG, J. Dynamic characteristics of functionally graded porous beams with interval material properties. Engineering Structures, 197, 109441(2019)
[10] GAO, K., HUANG, Q., KITIPORNCHAI, S., and YANG, J. Nonlinear dynamic buckling of functionally graded porous beams. Mechanics of Advanced Materials and Structures, 42(4), 1-12(2019)
[11] 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)
[12] CHEN, D., YANG, J., and KITIPORNCHAI, S. Nonlinear vibration and post buckling of functionally graded graphene reinforced porous nanocomposite beams. Composites Science and Technology, 142, 235-245(2017)
[13] CHEN, D., KITIPORNCHAI, S., and YANG, J. Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core. Thin-Walled Structures, 107, 39-48(2016)
[14] BAKSHI, S. R., LAHIRI, D., and AGARWAL, A. Carbon nanotube reinforced metal matrix composites——a review. International Materials Reviews, 55(1), 41-64(2013)
[15] BARTOLUCCI, S. F., PARAS, J., RAFIEE, M. A., RAFIEE, J., LEE, S., KAPOOR, D., and KORATKAR, N. Graphene-aluminum nanocomposites. Materials Science and Engineering, 528(27), 7933-7937(2011)
[16] ANSARI, R. and TORABI, J. Numerical study on the buckling and vibration of functionally graded carbon nanotube-reinforced composite conical shells under axial loading. Composites Part B, Engineering, 95, 196-208(2016)
[17] RAFIEE, M. A., RAFIEE, J., WANG, Z., SONG, H., YU, Z. Z., and KORATKAR, N. Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano, 3(12), 3884-3890(2009)
[18] YANG, J., WU, H., and KITIPORNCHAI, S. Buckling and post buckling of functionally graded multilayer graphene platelet-reinforced composite beams. Composite Structures, 161, 111-118(2017)
[19] WU, H., YANG, J., and KITIPORNCHAI, S. Dynamic instability of functionally graded multilayer graphene nanocomposite beams in thermal environment. Composite Structures, 162, 244-254(2017)
[20] SONG, M., KITIPORNCHAI, S., and YANG, J. Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Composite Structures, 159, 579-588(2017)
[21] GAO, K., GAO, W., CHEN, D., and YANG, J. Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation. Composite Structures, 204, 831-846(2018)
[22] KITIPORNCHAI, S., CHEN, D., and YANG, J. Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Materials and Design, 116, 656-665(2017)
[23] GAO, K., GAO, W., WU, B., DI, W. U., and SONG, C. Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales. Thin-Walled Structures, 125, 281-293(2018)
[24] GAO, K., GAO, W., DI, W. U., and SONG, C. Nonlinear dynamic stability of the orthotropic functionally graded cylindrical shell surrounded by Winkler-Pasternak elastic foundation subjected to a linearly increasing load. Journal of Sound and Vibration, 415, 147-168(2018)
[25] SOFIYEV, A. H. and KURUOGLU, N. Parametric instability of shear deformable sandwich cylindrical shells containing an FGM core under static and time dependent periodic axial loads. International Journal of Mechanical Sciences, 101-102, 114-123(2015)
[26] NGUYEN, D. K., NGUYEN, Q. H., TRAN, T. T., and VAN BUI, T. Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load. Acta Mechanica, 228(1), 141-155(2017)
[27] LEI, J., HE, Y., LI, Z., GUO, S., and LIU, D. Post-buckling analysis of bi-directional functionally graded imperfect beams based on a novel third-order shear deformation theory. Composite Structures, 209, 811-829(2019)
[28] ESMAEILZADEH, M. and KADKHODAYAN, M. Nonlinear dynamic analysis of axially moving porous FG plate subjected to local force with kinetic dynamic relaxation method. Computer Methods in Materials Science, 18(1), 18-28(2018)
[29] WANG, Y. Q. and YANG, Z. Nonlinear vibrations of moving functionally graded plates containing porosities and contacting with liquid:internal resonance. Nonlinear Dynamics, 90(2), 1461-1480(2017)
[30] LI, Y. H., DONG, Y. H., QIN, Y., and LV, H. W. Nonlinear forced vibration and stability of an axially moving viscoelastic sandwich beam. International Journal of Mechanical Sciences, 138-139, 131-145(2018)
[31] ZHOU, Y. F. and WANG, Z. M. Dynamic instability of axially moving viscoelastic plate. European Journal of Mechanics-A/Solids, 73, 1-10(2019)
[32] TAKABATAKE, H. A simplified analysis of rectangular floating plates subjected to moving loads. Ocean Engineering, 97, 37-47(2015)
[33] GAO, K., GAO, W., WU, D., and SONG, C. Nonlinear dynamic characteristics and stability of composite orthotropic plate on elastic foundation under thermal environment. Composite Structures, 168, 619-632(2017)
[34] VANDO, T., NGUYEN, D. K., DUC, N. D., DOAN, D. H., and BUI, T. Q. Analysis of bidirectional functionally graded plates by FEM and a new third-order shear deformation plate theory. Thin-Walled Structures, 119, 687-699(2017)
[35] SAHMANDI, S., AGHDAM, M. M., and RABCZUK, T. Nonlocal strain gradient plate model for nonlinear large-amplitude vibrations of functionally graded porous micro/nano-plates reinforced with GPLs. Composite Structures, 198, 51-62(2018)
[36] MOJAHEDIN, A., JABBARI, M., KHORSHIDVAND, A. R., and ESLAMI, M. R. Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory. Thin-Walled Structures, 99, 83-90(2016)
[37] ROBERTS, A. P. and GARBOCZI, E. J. Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Materialia, 49(2), 189-197(2001)
[38] EBRAHIMI, F. and DABBAGH, A. Vibration analysis of multi-scale hybrid nanocomposite plates based on a Halpin-Tsai homogenization model. Composites Part B:Engineering, 173, 106955(2019)
[39] ARANI, A. G., HAGHPARAST, E., and BABAAKBARZAREI, H. Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field. Physica B:Condensed Matter, 495, 35-49(2016)
[40] TURVEY, G. J. and SALEHI, M. Elastic-plastic large deflection response of pressure loaded circular plates stiffened by a single diametral stiffener. Thin-Walled Structures, 46, 991-1002(2008)
[41] GOLMAKANI, M. E. and KADKHODAYAN, M. Large deflection thermoelastic analysis of functionally graded stiffened annular sector plates. International Journal of Mechanical Sciences, 69, 94-106(2013)
[42] REZAEI-MOJDEHI, A., DARVIZEH, A., BASTI, A., and RAJABI, H. Three dimensional static and dynamic analysis of thick functionally graded plates by the meshless local Petrov-Galerkin (MLPG) method. Engineering Analysis with Boundary Elements, 35(11), 1168-1180(2011)
[43] AN, C. and SU, J. Dynamic response of clamped axially moving beams:integral transform solution. Applied Mathematics and Computation, 218(2), 249-259(2011)
[44] CONG, P. H. and DUC, N. D. New approach to investigate the nonlinear dynamic response and vibration of a functionally graded multilayer graphene nanocomposite plate on a viscoelastic Pasternak medium in a thermal environment. Acta Mechanica, 229(9), 3651-3670(2018)
Outlines

/

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