Нелинейные свободные колебания многослойных пологих оболочек симметричного строения со сложной формой плана

Abstract

To investigate nonlinear free vibrations of the laminated shallow shells with complex plan form a new method is proposed. The mathematical statement is carried out by first-order shear deformation theory like Timoshenko theory. The distinctive feature of this approach is application of the R -functions theory and variational methods for finding eigenfunctions. These functions are used as basis functions for solving a nonlinear problem. To check the validity of the proposed method some test problems have been solved. New numerical results have been obtained for spherical shallow shells with complex plan form as the backbone curves.