Free Vibration Analysis of Cracked Orthotropic Rectangular Plates Under Thermal Effect

Abstract

This paper presents the free vibration analysis of orthotropic rectangular plates with line surface cracks under thermal conditions. The classical plate theory is employed to derive the governing equation of cracked plates, in which the surface cracks located at the plate center are formulated based on a line-spring model. It is assumed that a thermal load is uniformly distributed on the plates throughout its volume, and thus the moments of the plates resulted by the thermal effect are neglected. The deduced governing equation is solved by the discrete singular convolution (DSC) method with the Shannon’s delta kernel. The DSC technique is a relatively new method for vibration analysis of plates. It not only possesses flexibility in handling complex geometries and boundary conditions, and also holds a high-level of accuracy. In this study, the treatment for orthotropic cracked plates with various combinations of boundary conditions, namely, simply supported, clamped and free edges is studied. The results are compared with the existing solutions to verify the correctness and reliability. Some first-known results are also presented.