FORCED VIBRATIONS OF A CLAMPED, CIRCULAR PLATE OF RECTANGULAR ORTHOTROPY

✍ Scribed by C. PISTONESI; P.A.A. LAURA

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 82 KB
• Volume: 228
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1999.2462

✦ Synopsis

In the case of free vibrations of a circular plate of rectangular orthotropy the vibration analyst encounters severe di$culties. Analytical, exact solutions appear possible in some instances [1]. Useful, approximate solutions are available [2}7]. Free vibrations of thin and elastic plates of complicated boundary shape of rectangular orthotropy have also been studied [8,9]. On the other hand, apparently, forced vibrations have not been previously considered. This note deals with an approximate treatment of the title problem in the case where the plate is subjected to a!p cos t-type excitation. The Galerkin method is employed.

2. APPROXIMATE ANALYTICAL SOLUTION

Forced vibration of the clamped orthotropic circular plate are described by the di!erential system (see Figure 1)

1. and, in polar co-ordinates the boundary conditions are w(a, t)" *w *r (a, t)"0. (2a,b) Making w(x, y, t)"=(x, y) cos t (3) and substituting in equation (1) one obtains D *= *x #2D *= *x*y #D *= *y !p ! h ="0.

(4)