Non-Linear Vibration Analysis Of Arbitrarily Laminated Thin Rectangular Plates On Elastic Foundations

✍ Scribed by Y.-S. Shih; P.T. Blotter

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 582 KB
• Volume: 167
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1993.1347

✦ Synopsis

Solutions to free undamped large amplitude vibrations of arbitrarily laminated thin rectangular plates on elastic foundations, based on an assumed mode shape, are determined. Simply supported and clamped boundary conditions with both movable and immovable edges are considered. The governing equations of motion of plates on linear Winkler, Pasternak foundations and a non-linear Winkler foundation are provided using von Kármán's theory. The Galerkin's method reduces the von Kármán equation to a time dependent ordinary differential equation. Solutions are then obtained and compared using the Runge-Kutta method, the direct numerical integration method and the perturbation method. The effects on the non-linear frequency of several parameters such as amplitude, material lamination, aspect ratio, boundary conditions as relate to movable and immovable edges, and the influence of elastic foundation constants are provided.