Vibraciones de Membranas de Forma Arbitraria a través de una Solución Generalizada

Abstract

The natural vibrations of arbitrary shaped membranes under tension are studies using the Whole Element Method (WEM) developed by the authors for boundary problems in 1D, 2D and 3D. The method is based in proposing extended trigonometric series in unitary domains. Since here we are dealing with arbitrary shaped domains, a suitable transformations becomes necessary. Then the governing functional is substantially modified. Theorems and corollaries which form the basis of WEM do not pose any restriction to the functional. Then arbitrary precision frequencies and uniform convergent mode shapes may be obtained. Several examples illustrate the application. The solution of polygonal membranes allows by means of the well-known analogy to find similar supported plates frequencies. This is not the case when curved borders exist. Results are compared with values of other authors and results obtained using the Finite Element Method.