Nonlinear free vibrations of multilayer shallow shells with a symmetric structure and with a complicated form of the plan

We propose a method to study free nonlinear vibrations of multilayer shallow shells with a complicated form of the plan. The mathematical statement of the problem is realized in the frame of a refined firstorder theory of the Tymoshenko type. A distinctive specific feature of the work is the application of the theory of R -functions and variational methods to the determination of eigenfunctions used as the basis in the construction of the required solution of a nonlinear problem. The proposed method is tested, and some new problems are solved. As a result, we constructed the amplitude–frequency dependences for spherical shells with a complicated form of the plan.