Journal of Aeronautical Engineering

Journal of Aeronautical Engineering

Effect of small scale on nonlinear vibrations of viscoelastic circular microplate rested on nonlinear viscoelastic foundation

Document Type : Original Article

Authors
Mehdi Moayeri 1
Babak Darabi 2
Ahmad Hoseini Sianaki 3
Armen Adamian 3
1 1. Ph.D. Student, Department of Mechanics ,Faculty of Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
2 Department of Mechanics ,Faculty of Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
3 Assistant Prof., Department of Mechanics ,Faculty of Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
10.22034/joae.2022.344528.1100
Abstract
In this paper, the nonlinear free vibrations of viscoelastic solid and annular circular microplates are investigated. These microplates are rested on a viscoelastic symmetrical and asymmetric nonlinear foundations. The small scale effect is considered using the modified coupling stress theory. The nonlinear equations of the microplates is obtained using Hamilton's principle and first order shear deformation theory (FSDT). The finite element method (FEM) and Newton iteration algorithm are used to obtain the nonlinear natural frequency. The obtained results are compared with the results of the researchers and a good agreement is observed between them. Then, the effects of various parameters such as length scale parameter, outer radius to thickness ratio, maximum deflection to thickness ratio, softening and hardening nonlinear foundation, symmetric and asymmetric nonlinear foundation, different boundary conditions, structure and foundation damping were investigated. The results show that free and clamped boundary conditions have the highest and lowest nonlinear frequencies of solid and hollow circular microplates, respectively. Also, symmetric and asymmetric nonlinear viscoelastic foundations have a significant effect on the nonlinear nonlinear frequency and the nonlinear frequency of the hollow circular microplate changes to higher values for each amplitude ratio in the presence of a hardened asymmetric foundation.
Keywords
Nonlinear free vibrations, solid and annular circular microplates, nonlinear viscoelastic foundation
Modified couple stress theory, first order shear deformation theory
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Journal of Aeronautical Engineering
Volume 24, Issue 2
April 2022
Pages 152-166

  • Receive Date 28 May 2022
  • Revise Date 22 July 2022
  • Accept Date 25 July 2022