Vibration Analyses of Cracked Plates By the Ritz Method With Moving Least-squares Interpolation Functions

The solutions for the vibrations of cracked thin plates are obtained by the Ritz method with admissible functions. Based on the classical plate theory, the basis functions comprising polynomials and crack functions are adopted to generate the admissible functions by the moving least-squares approach for a set of nodes randomly distributed in the domain. The crack functions account for the singular behaviors of stress resultants at crack tip(s), which are discontinuous in displacement and slope across the crack. The present solutions are validated through convergence tests of frequencies and by comparison with the published results for simply-supported cracked rectangular plates. The solutions are further employed to determine the natural frequencies of cantilevered skewed rhombic and isosceles triangular plates and completely free circular plates, each with a crack of varying length, location and orientation. The numerical results are tabulated and some corresponding mode shapes are also presented, by means of nodal patterns. Most of the results shown here are new to the literature.