A perturbation approach for the eigenfrequency analysis of separable Kirchhoff thin-plate problems on a rectangle

✍ Scribed by Matthew P. Coleman; Laura A. McSweeney

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 221 KB
• Volume: 292
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1016/j.jsv.2005.08.013

✦ Synopsis

We introduce a method for the estimation of the eigenfrequencies for separable Kirchhoff thin-plate problems on a rectangle, particularly those involving the free boundary condition. We believe that this paper is the first to give such a treatment for the low end of the spectrum. The method is an adaptation of an asymptotic/perturbation method used for the treatment of various beam problems and, in the setting of the plate, is shown to be a generalization and refinement of the asymptotic methods of Bolotin and Keller and Rubinow (the wave propagation method). We compare our results with those of our own Legendre-tau approximation and, where available, with numerical results extant in the literature. Excellent agreement is found in each case.