Nonlinear modes of motion of thin circular cylindrical shells

Free flexural vibrations of a simply supported shell are studied within the framework of the nonlinear theory of flexible shallow shells. It is assumed that large-amplitude flexural vibrations are coupled with radial vibrations of the shell. Modal equations are derived by the Bubnov–Galerkin method. Periodic solutions are obtained by the Krylov–Bogolyubov method. The skeleton curve of the soft type obtained using a nonlinear finite-dimensional shell model agrees with available experimental data.