An extended separation-of-variable method for the free vibration of orthotropic rectangular thin plates

This paper proposes a method to solve for closed-form analytical solutions of the free vibration problems of orthotropic rectangular thin plates with arbitrary homogeneous boundary conditions. This proposed method is called the extended separation-of-variable method, in which the mode functions are in a separation-of-variable form, and the frequencies in two spatial directions are mathematically independent of each other. The closed-form analytical eigensolutions satisfy the Rayleigh's principle exactly. Unlike the extended Kantorovich–-Krylov method, the proposed method solves all eigenvalue equations of two directions simultaneously, not iteratively. Numerical experiments validate the proposed method. More importantly, the proposed method is applicable to any eigenvalue problems of plates, shells, three-dimensional plates and cubes.