A closed-form solution for fully simply supported rectangular thin plates containing crack

In this Paper, exact closed-form characteristic equation in explicit forms are presented on the basis of classical plate theory for freely vibration of rectangular simply supported thin plates with an arbitrary number of allover part-through cracks. The crack is assumed nonpropagating and perpendicular to both edges. It was also assumed that the crack is open at all dynamical condition to avoid non-linearity. A continuously distributed line-spring model was used to describe the elastic behavior of the all-over part-through crack. The accuracy of the presented solution was confirmed by comparing with the results of finite element method using ABAQUS FE code. In addition, the effect of the crack depth and crack location on the natural frequencies of rectangular thin plates was investigated in tabular and graphical forms. The effects of the modes II and III loading conditions (shearing and tearing modes of crack deformation) on the natural frequencies were studied when the crack is located at the nodal lines. Finally, fundamental frequency parameters of thin rectangular plate with an arbitrary number of cracks were obtained.

Keywords:

free vibration , rectangular plate , partthrough crack