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

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.