Nonlinear vibrations of circular plates with notches. Method of R-functions

Abstract

We investigate vibrations of geometrically nonlinear circular plates with two notches. For the determination of natural frequencies of vibrations, the method of R-functions is used. Nonlinear vibrations of a plate are expanded in eigenmodes of linear vibrations containing R-functions. As a result of using the Bubnov–Galerkin method, we obtain a dynamic system with three degrees of freedom, which is investigated by the method of multiple scales.