Free Vibration Analysis of Rectangular Plates with Interior Point Supports

• Main Authors: Shaw Pying Lee, 李紹平
• Other Authors: Lin-Tsang Lee
• Format: Others
• Language: en_US
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/82981605010063632833

碩士 === 國立中興大學 === 應用數學研究所 === 81 === A single domain application of the impulse function approach is used to study the free, flexural vibration problems of Levy- type plates with arbitrary interior point supports. This analysis is based on the representation of the concentrated reactions at the point support locations by a double Fourier sine series expansion of the impulse function. This study provides an extension of the classical Levy's solution in the vibration analysis of plate with interior point supports. The extended solution allows one to solve the problem in a single domain in contrast to the multiple domain solutions available in the literature. This new approach can greatly reduce the complexities of the problems involving arbitrary multiple point supports. The versatility and ability of this approach is demenstrated by considering a rectangular plate with two opposite edges simply supported and classical boundary conditions (free, clamped or simply supported) on the other two edges. The simulation of interior point supports in plates provides a method for presenting the discrete discontinuities in the force field, in the interior of plate, into the governing differential equation and obtaining a concise representation of the solution in a single domain of plate. Numerical results are presented for a number of specific problems, including the convergence and accuracy of the approach, which include natural frequencies and mode shapes of some typical plates with interior point supports. The reults obtained by using the single domain approach are compared with those obtained by using the multiple domain approaches in the literature.