Free Vibration Analysis of Rhombic Plate with Central Crack

Abstract

In this paper, free vibration analysis of rhombic plate with pre-existing central crack has been done using the finite element method. The Mindlin theory of plate has been used in the process of investigation. The following six boundary conditions at the edges of the plate have been considered. They are simply supported at all edges (SSSS), clamped at all edges (CCCC), free at all edges (FFFF), clamped-simply supported (CSSC), clamped-free (CFFC), and clamped-free-simply supported (CSFS). Effects of crack length on natural frequencies of rhombic plate with different skew angles i.e. 15• , 30• , 45• , 60• have been studied. It is observed that percentage drop in fundamental frequency due to presence of central crack in the rhombic plate increases with an increase in skew angle for CCCC, SSSS, and CSSC edge conditions at a given crack ratio (non-dimensional crack length). Under the CFFC, CSFS, and FFFF edge conditions, percentage drop in natural frequency of rhombic plate is very small for crack ratio of 0.2 at different skew angles. In case of the CFFC edge condition of the rhombic plate, percentage drop in fundamental frequency is within 0.7% at all skew angles and with all crack ratios considered. Some of the results obtained by the present method have been compared with the published results. Most of the results obtained are novel for rhombic crack plate.

Effect of crack on free vibration of a pre-stressed curved plate

“…1 Xue and Wang 2 studied the free vibration of a flat plate with a side crack of Mode I fracture, reinforced by one stiffener parallel to the edges of the plate. Azam et al 3 used the Mindlin theory of plate to do free vibration analysis of a rhombic plate with preexisting central crack using the finite element method. Chang proposed new sets of improved basis functions for in-plane and out-of-plane displacements of square plates that can yield proper functions for the Ritz method based on the classical thin plate theory.…”

Three-Dimensional Free Vibration Analyses of Preloaded Cracked Plates of Functionally Graded Materials via the MLS-Ritz Method

“…On the basis of the classical plate theory (CPT), these studies have used analytical methods [24,25], the integral equation approach [26,27], the Ritz method [28][29][30][31], the generalized differential quadrature method [32,33], Galerkin's method [34], the mesh-free approach [35], and the FEM [36,37] to investigate the aforementioned vibrations. Based on the first-order shear deformation plate theory (FSDT), studies have developed various approaches, such as the Ritz method [38,39], mesh-free method [40], FEM [41,42], and extended FEM (XFEM) [43,44], while Singh et al [45] used an extended isogeometric approach based on a higher-order shear deformation plate theory.…”

Free vibration analysis of cracked plates using peridynamics

“…(2018) performed free vibration analysis of square center-cracked plate at various orientations using finite element method. Azam et. al.…”