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

A separation-of-variable method was proposed in 2009 by the present authors and co-workers (Xing YF, Liu B. New exact solutions for free vibrations of thin orthotropic rectangular plates. Compos Struct 2009;89:567–74), but this traditional separation-of-variable method is incapable for free boundary conditions. Hence, this work is to improve the traditional separation-of-variable method to make it capable of dealing with free boundary conditions. This new method is called the improved separation-of-variable method, in which the characteristic differential governing equation is solved directly, and the free boundary conditions also have separable forms, which are achieved with the Rayleigh’s variational principle. In addition, the relationships between spatial eigenvalues and temporal eigenvalue are quite concise. For plates without free edges, the proposed method reduces to the traditional separation-of-variable method. Numerical experiments validate the improved method. The present technique of handling free boundary conditions is a general methodology for eigenvalue problems such as free vibration and eigenbuckling.