Nonobvious features of dynamics of circular cylindrical shells

Abstract

In the framework of the nonlinear theory of flexible shallow shells, we study free bending vibrations of a thin-walled circular cylindrical shell hinged at the end faces. The finite-dimensional shell model assumes that the excitation of large-amplitude bending vibrations inevitably results in the appearance of radial vibrations of the shell. The modal equations are obtained by the Bubnov-Galerkin method. The periodic solutions are found by the Krylov-Bogolyubov method. We show that if the tangential boundary conditions are satisfied “in the mean,” then, for a shell of finite length, significant errors arise in determining its nonlinear dynamic characteristics. We prove that small initial irregularities split the bending frequency spectrum, the basic frequency being smaller than in the case of an ideal shell.