Spline-based investigation of natural vibrations of orthotropic rectangular plates of variable thickness within classical and refined theories

A spline-collocation approach is proposed for studying the natural vibrations of orthotropic rectangular plates of variable thickness.The approach is based on the spline-approximation method and the method of discrete orthogonalization coupled with the step-by-step search method.The study is carried out within the framework of the classical and refined theories of plates.The dynamic response of the plates is studied depending on the variation of the plate thickness, the mechanical parameters, and the type of boundary conditions.