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 authors propose new numerical-analytical method. According to this approach the initial problem is reduced to consequences of some linear problems including linear vibrations problem, special elasticity problem and nonlinear system of ordinary differential equations in time domain. Linear problems are solved by variational Ritz method and Bubnov-Galerkin procedure combined with the R-functions theory. To construct the basic functions that satisfy all boundary conditions in case of simply-supported shells we propose new solution structures. The proposed method is used to solve both test problems and the new ones.
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