Free vibrations of flexible shallow shells of complex shape

A method is proposed for studying the free vibrations of flexible shallow shells with a complex planform. The method is based on variational and R-function methods. The R-function method allows constructing a system of basis functions in an analytic form. This makes it possible to reduce the Donnell-Mushtari-Viasov equations to Duffing equations. The amplitude-frequency characteristics of shallow shells with a complex planform are given for different curvatures and boundary conditions. The results obtained are compared with published results for simply supported square shells to demonstrate the reliability and efficiency of the method.