R-function method in problems of investigations of geometrically non-linear vibrations of shallow shells

Free geometrically nonlinear vibrations of plates and shallow shells with complicated planforms are studied. The algorithm is based on the application of the R-function theory and the Bubnov – Galerkin procedure to the equations of motion of shallow shells, that allows to reduce them to the second-order ordinary differential equation in the case of complicated planforms shells and different types of boundary conditions. The backbone curves for shallow shells with simple and complex planforms are presented. The results obtained are compared with that available from other works