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Acta Mechanica

, Volume 229, Issue 9, pp 3651–3670 | Cite as

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

  • Pham Hong Cong
  • Nguyen Dinh DucEmail author
Original Paper
  • 108 Downloads

Abstract

This paper presents an analytical approach to investigate the nonlinear dynamic response and vibration of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene platelets (GPLs) using first-order shear deformation theory and a stress function with full motion equations (not using Volmir’s assumptions). The weight fraction of GPL nanofillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC). The modified Halpin–Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young’s modulus of the GPLRC layers. The plate is assumed to rest on a viscoelastic Pasternak medium and to be subjected to dynamic mechanical load in a thermal environment. Numerical results for the nonlinear dynamic response and vibration of functionally graded (FG) multilayer GPLRC plates are obtained by the Runge–Kutta method. The results show the influences of the GPL distribution pattern, weight fraction, geometry, foundation models, mechanical and temperature loads on the nonlinear dynamic response and vibration, natural frequencies and frequency–amplitude curves of FG multilayer GPLRC plates.

List of symbols

\(E_\mathrm{GPL} , E_\mathrm{m} \)

The Young’s moduli of the GPL and matrix, respectively

\(a_\mathrm{GPL} ,b_\mathrm{GPL} ,t_\mathrm{GPL}\)

The length, width and thickness of GPL nanofillers, respectively

\(v_\mathrm{GPL} ,v_\mathrm{m} \)

The Poisson’s ratios with the subscripts “GPL” and “m” referring to the GPL and matrix, respectively

\(\alpha _\mathrm{GPL} ,\alpha _\mathrm{m} \)

The thermal expansion coefficients with the subscripts “GPL” and “m” referring to the GPL and matrix, respectively

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Notes

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Advanced Materials and Structures Laboratory, VNU-HanoiUniversity of Engineering and Technology (UET)HanoiVietnam
  2. 2.Centre for Informatics and Computing (CIC)Vietnam Academy of Science and TechnologyHanoiVietnam
  3. 3.Department of Civil and Environmental EngineeringSejong UniversitySeoulSouth Korea
  4. 4.Infrastructure Engineering Program, VNU-HanoiVietnam-Japan University (VJU)HanoiVietnam

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