Geometrical analysis of vibrations of functionally graded shell panels using the R-functions theory

Abstract

An approach for investigation of geometrically nonlinear vibrations of functionally graded shallow shells and plates with complex planform is proposed. It combines the application of the R-functions theory (RFM), variational Ritz’s method, the procedure by Bubnov-Galerkin and Runge-Kutta method. The presented method is developed in the framework of the first–order shear deformation shallow shell theory (FSDT). Shell panels under consideration are made from a mixture of ceramics and metal. Power law of volume fraction distribution of materials through thickness is chosen. Investigation of nonlinear vibrations of functionally graded shallow shells and plates with arbitrary planform and different types of boundary conditions is carried out. Test problems and numerical results have been presented for one-mode approximation in time. Effect of volume fraction exponent, geometry of a shape and boundary conditions on the natural frequencies is brought out