Large -amplitude nonlinear free vibrations of functionally graded plates with porous imperfection: A novel approach based on energy balance method

A novel approach, based on energy balance method, to deal with the large-amplitude nonlinear free vibration problem of the rectangular porous functionally graded plates is presented in this paper. Both even and uneven porosity distributions are considered. The governing equations of the plates are established via von Kármán theory and Lagrange equation. A new deformation assumption for the vibration problem of plates is proposed. This deformation assumption allows a quadratic relationship between the in-plane and out-plane displacements, thus is more advantageous than the conventional one to describe the displacement field of the plate during the vibration period. The nonlinear frequency of the plate is obtained by adopting the energy balance method cooperating with the Newton-Raphson iterative method. Numerical examples are provided to inspect the influences of the porosity distribution type, porosity volume fraction, geometrical parameters and vibration amplitude on the nonlinear free vibration characteristic of the plates. The results indicate that the nonlinear-to-linear frequency ratio is less sensitive to the porosity volume fraction than the linear frequency for the porous functionally graded plates, and the nonlinear-to-linear frequency ratio of plate with uneven porosity distribution is more sensitive to the porosity volume fraction than that with even porosity distribution. © 2020 Elsevier Ltd