A study on annular plates with radial through cracks by means of sector type element

Abstract

In this study, the natural frequencies of annular plates with periodic radial through cracks are investigated by means of finite element method. The position of the crack in the plate surface was selected as parallel to radial direction. Both the cracks emanating from the inner and outer boundary of the plate is non-propagating and open. The crack in the element was modeled by an additional flexibility matrix, the terms of which were calculated using fracture mechanics. For this purpose, an isoparametric sector type element with radial through crack of four nodes and three degrees of freedom at each node is considered. In the event of the selection of appropriate half sector angle, taking into account the closeness of the geometries of the sector and trapezoidal type element, the flexibility matrix of the sector type element with crack are derived by means of the flexibility matrix of the trapezoidal type element. The natural frequencies of annular plates are found for different length and number of cracks. The theoretical results are obtained with different boundary conditions. The obtained results of improved elements are compared with experimental results in the literature. It is observed that the increment of the length and number of cracks has various effects on the natural frequencies and mode shapes of the annular plate.