Application of the R-function method to nonlinear vibrations of thin plates of arbitrary shape

In this paper free large-amplitude flexural vibrations of thin plates with various planforms and boundary conditions are studied by the R-function method. This method is based on the joint application of the R-function theory and variational methods. The main feature of the R-function theory is the possibility to present all geometric information given in the boundary value problem in analytical form, which allows one to seek a solution in the form of some formula called the solution structure. A method of constructing the solution structures for the given nonlinear vibration plate bending problems is developed. Numerical examples of large-amplitude flexural vibrations of thin plates with arbitrary shapes and boundary conditions for illustrating the aforementioned R-function method and comparison against the other methods are made to demonstrate its merits and advantages.