Vibration Mode Localization in Rectangular Plates with V-Shaped Through Cracks

A solution method is presented for the free vibration analysis of rectangular plates with V-shaped through cracks. A domain decomposition technique is employed in combination with two sets of modified Fourier series which are applicable to elastic boundary conditions, and the continuity conditions at interconnecting boundaries of the subdomains are enforced by translational and rotational springs with zero or infinite stiffness. The Rayleigh-Ritz method is employed to determine the generalized coordinates and the corresponding natural frequencies, and the mode shapes are then constructed by superposition of the admissible functions. The main advantage of the proposed method lies in its applicability to various combinations of boundary conditions and crack configurations. Numerical examples are given to verify the convergence of the proposed method, in which the results obtained are compared with those from FEM (ANSYS). Finally, this method is employed to determine the modal characteristics of plates with V-shaped cracks by focusing on the effects of various crack parameters on mode localization and frequencies. It is found that the frequencies and mode shapes are more affected by longer crack lengths, smaller included angles, and stiffer boundary constraints, and that mode localization is more likely to occur under these conditions.