Vibrations of Plates and Shells with Attached Mass - L. U. Sultanov; I. R. Garifullin (Учёные записки Казанского университета: Серия Физико-математические науки)
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.