Nonlinear free vibration of rotating FG trapezoidal microplates in thermal environment

The size-dependent nonlinear free vibration characteristics of rotating functionally graded (FG) trapezoidal microplates are investigated based on a four variable refined plate theory (FVRPT) coupled with the modified strain gradient theory (MSGT). The geometric nonlinear strain–displacement relations are derived by considering the von Kármán geometric nonlinearity hypothesis. The material composition is assumed to be graded in the thickness direction according to the power law function. The properties of the constituent materials are assumed temperature-dependent and the effective material properties are determined by employing Mori–Tanaka micromechanical homogenization technique. By applying the Chebyshev–Ritz method, the system of nonlinear equations governing the nonlinear free vibration characteristics of rotating trapezoidal FG microplates is derived. The nonlinear frequencies are determined through a direct iterative process by considering both positive and negative deflection cycles. Through the numerical investigations, the effects of different geometric and material parameters on the nonlinear to linear frequency ratio are studied and discussed. The results show that the rectangular-shaped microblades have greater frequencies than the trapezoidal ones. Also, it is found that the temperature rise has hardening effect, meanwhile the length scale parameter has softening effect on the variations of the frequency ratio versus amplitude ratio.