Vibrations of Plates and Shells with Attached Mass

Abstract

The problem of vibrations of plates and shells with a mass attached to the point was solved. A mathematical model was developed based on the hypothesis of nondeformable normals. The latter was used to derive a system of resolvable dynamic equations for the shell with a mass, where the unknowns are the dynamic deflection and stress function. The problem was solved numerically and analytically. In accordance with the boundary conditions, the shell deflection was expressed as double trigonometric series. The transition from the initial dynamic system to the solution of the final system of nonlinear ordinary differential equations was achieved by the Bubnov–Galerkin method. For time integration, the finite difference method was used.