Closed-form solutions for free vibration of rectangular nonlocal Mindlin plates with arbitrary homogeneous boundary conditions

In this paper, an extended separation-of-variable (SOV) method is developed to achieve the closed-form solutions for free vibration of rectangular nonlocal Mindlin plates with arbitrary homogeneous boundary conditions. With the weighted residual notion, the amplitude of the potential energy functional and the kinetic energy coefficient are derived, then the Rayleigh's principle is formulated for the nonlocal Mindlin plates. In accordance with the principle, the extended SOV method is realized. In the present method, the mode functions are in a separation-of-variable form and the natural frequencies corresponding to two-direction mode functions are considered to be independent in a mathematical sense. Numerical comparison results verify the correctness and accuracy of the present method. Moreover, the effects of nonlocal parameter, boundary conditions and thickness ratio on the free vibration are discussed comprehensively.