INTRODUCTION OF MODIFIED COMPARISON FUNCTIONS FOR VIBRATION ANALYSIS OF A RECTANGULAR CRACKED PLATE

In this paper, new functions named “modified comparison functions” are introduced and used for vibration analysis of a simply supported rectangular cracked plate. It is assumed that the crack having an arbitrary length, depth and location is parallel to one side of the plate. Elastic behavior of the plate at crack location is considered as a line spring with a varying stiffness along the crack. Because there is no exact solution for this problem, one has to use some approximate methods. Although among the functions which are used for vibration analysis of a cracked plate, the comparison functions are more accurate, obtaining these functions is very difficult. In spite of this difficulty, a method for obtaining the comparison functions of the above cracked plate satisfying all the geometric and natural boundary conditions as well as the inner boundary conditions at crack location is introduced. The main purpose of this paper is to improve the accuracy of these comparison functions which only satisfy all the boundary conditions and the inner boundary conditions at the crack location, but their accuracy is questionable at a distance away from the boundaries. In order to increase the accuracy of the comparison functions, it is assumed that the crack affects the mode shape functions in its neighborhood, and its maximum influence is at the crack location, and the influence will vanish at a sufficient distance from the crack. The comparison functions obtained in this way are called the “modified comparison functions” and they are more accurate than the comparison functions. Using the Rayliegh–Ritz method, the “modified comparison functions” are used to obtain the natural frequencies of the cracked plate mentioned above. The results are presented by appropriate curves showing the variations of the natural frequencies of the cracked plate in terms of the crack depth, length and location.