Application of Rayleigh-Ritz and Galerkin methods to non-linear vibration of plates

✍ Scribed by C.P. Vendhan; Y.C. Das

• Publisher: Elsevier Science
• Year: 1975
• Tongue: English
• Weight: 595 KB
• Volume: 39
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/s0022-460x(75)80214-8

✦ Synopsis

The difference between the three variational equations of motion and the dynamic analogue of the yon Karman equations governing the non-linear vibration of plates is considered in the context of the Rayleigh-Ritz and Galerkin methods. The non-linear free vibrations of two types of plates with in-plane constraints are considered as examples. In the analysis a single mode expansion is assumed for the transverse displacement and the in-plane inertia terms are neglected. The convergence of the non-linear time period is studied by increasing the number of terms in the modal expansions for the in-plane displacements. It is observed that the Rayleigh-Ritz and Galerkin approximations converge from opposite directions, thus suggesting a possible approach to bound the solutions on either side. The general significance of this observation is discussed.