A COMPARATIVE ANALYSIS OF THE BEAM LENGTH EFFECT ON FREE VIBRATION OF CRACKED BEAMS

Abstract

The aim of this study is to investigate the effect of beam length on free vibration behavior of cracked Euler-Bernoulli and Timoshenko beams by using an analytical approach based on the flexibility coefficients and local stiffness matrix. Expressions were derived for determining the mode shapes and natural frequencies. In order to test the presented modeling technique and the results from analytical solution and finite element analysis, natural frequencies and mode shapes were computed for various crack locations and depths, and compared with each other and those reported in literature. The presence of a crack causes a local variation of stiffness and affects the mechanical behavior of the entire structure. Reduction in the stiffness reduces the natural frequencies and affects the mode shapes. Crack depth and its relative position have got major effects on dynamic behavior of the beam. Vibration measurements offer a non-destructive, inexpensive and fast means to detect and locate cracks. Methods allowing early detection and localization of cracks have been the subject of intensive investigation over the last two decades. Various kinds of analytical (Khaji, 2009), numerical (Patil, 2003; Zheng, 2004; Shifrin, 1999) and experimental (Lele, 2001; Nahvi, 2005) investigations upon dynamic behavior of cracked structures have been studied by many researchers. In this paper the local stiffness of the cracked section was calculated by using some formulations in fracture mechanics (zer, 2011). The cracked element stiffness matrix was constructed and then assembled with the matrix of non-cracked elements of the structure (Tada, 1973). A computer program using MATLAB was prepared to determine the natural frequencies and mode shapes of the cracked beams. In addition, finite element analysis was performed using finite element code ANSYS. In order to test the presented modeling technique and the results from analytical solution and finite element analysis, natural frequencies and mode shapes were computed for various crack locations and depths, and compared with each other and others from literature (Lele, 2001).