Dynamics of shallow shells with geometrical nonlinearity interacting with fluid

The vibrations of the shallow shell with geometrical nonlinearity submerged in a fluid are considered. Interaction of the shell with a fluid is described by linear hypersingular integral equation, which is solved by the boundary element method. The vibrations of the shell are described by the nonlinear finite-degree-of-freedom system. The vibrations are studied by the Shaw–Pierre nonlinear modes.