Vibration Analysis of Corner Supported Mindlin Plates of Arbitrary Shape Using the Lagrange Multiplier Method

✍ Scribed by S. Kitipornchai; Y. Xiang; K.M. Liew

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 400 KB
• Volume: 173
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1994.1241

✦ Synopsis

This paper presents the first known solutions of the problem of free flexural vibration of corner supported Mindlin plates of arbitrary shape. A hybrid numerical approach combining the Rayleigh-Ritz method and the Lagrange multiplier method has been developed to solve the plate vibration problem. The algorithm uses the (p b-2) shape functions to account for different geometries, and Lagrange multipliers to impose zero lateral deflection constraints at plate corners. The method of solution is applicable to arbitrarily shaped plates with corner supports. In this paper, however, only triangular, skew and annular sector plates are chosen for the purpose of demonstration. Some comparison studies for corner supported thin square plates are made to verify the accuracy of the derived solutions.