Studying the free vibrations of multilayer plates with a complex planform

An efficient method is developed to solve the free-vibration problems for arbitrarily shaped orthotropic multilayer plates in a refined formulation. The method is based on the R-function and Ritz methods. Sequences of coordinate functions satisfying kinematic boundary conditions are constructed in an analytic form. The method is used to solve the vibration problem for multilayer square and arbitrarily shaped plates. The results obtained for square plates are analyzed. A comparison of these results with those available in the literature demonstrates the efficiency of the method