VIBRATION ANALYSIS OF MEMBRANES AND PLATES BY A DISCRETE LEAST SQUARES TECHNIQUE

✍ Scribed by P. Žitňan

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 245 KB
• Volume: 195
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1996.0448

✦ Synopsis

A discrete least squares technique for computing the free transverse vibrations of membranes and plates is presented. The proposed technique consists of two steps. In the first step a quadratic matrix eigenvalue problem resulting from the minimization of a discrete residual error function is solved. If the accuracy of the eigenvalue approximations is not sufficient, these initial approximations can be improved by using the Gauss-Newton method. Numerical results concerning the vibration of the fixed circular membrane, fixed circular membrane with circular ridges and clamped circular plate are reported. As shown, the trial functions need not satisfy any of the prescribed boundary conditions, which makes possible the vibration analysis of membranes and plates with complicated shape. At the end of the paper a short discussion is given on how to use the proposed technique in solving problems of higher complexity, and some possible directions in the development of this technique are outlined.