Abstract
A first endeavor is made to obtain the analytical free vibration solutions of orthotropic rectangular thin plates utilizing the generalized integral transformation technique. Owing to the nature of the problem, it is very hard to get the exact solution of the title problem by common inverse/semi-inverse method. In solution procedure, the vibrating beam function is selected as the integral core to form the generalized integral transformation pair. Then, the high order partial differential equation under specific boundary conditions is converted to linear algebraic equations and the exact solution is achieved in a straightforward way. One of the advantages of the proposed method is its simplicity and versatility and does not require pre-determining the deflection function which makes the solving procedure more reasonable. The method has wide applications range and can handle other elastic plate problems, such as shear buckling, buckling, and bending. The present results are validated by comparing with the existing analytical solutions which show satisfactory agreement.
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