The R-function method for the free vibration analysis of thin orthotropic plates of arbitrary shape

Free flexural vibrations of homogeneous, thin, orthotropic plates of an arbitrary shape with mixed boundary conditions are studied using the R-function method. The proposed method is based on the use of the R-function theory and variational methods. In contrast to the widely used methods of the network type (finite differences, finite element, and boundary element methods), in the R-function method all the geometric information given in the boundary value problem statement is represented in an analytical form. This allows one to seek a solution in a form of some formulas called a solution structure. These solution structures contain some indefinite functional components that can be determined by using any variational method. A method of constructing the solution structures satisfying the required mixed boundary conditions for eigenvalue plate bending problems is described. Numerical examples for the vibration analysis of orthotropic plates of complex geometry with mixed boundary conditions for illustrating the aforementioned R-function method and comparison against the other methods are made to demonstrate its merits.