Investigation of Geometrically Nonlinear Vibrations of Laminated Shallow Shells with Layers of Variable Thickness by Meshless Approach

Abstract

Geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness are studied. Nonlinear equations of motion for shells based on the first order shear deformation and classical shells theories are considered. In order to solve this problem we use the numerically-analytical method proposed in work [1]. Accordingly to this approach the initial problem is reduced to consequences of some linear problems including linear vibrations problem, special elasticity ones and nonlinear system of ordinary differential equations in time. The linear problems are solved by the variational Ritz’ method and Bubnov-Galerkin procedure combined with the R-functions theory [2]. To construct the basic functions that satisfy all boundary conditions in case of simply-supported shells we propose new solutions structures. The proposed method is used to solve both test problems and new ones.