Int. J. of Intelligent Computing and Applied Sciences 72 Copyright©2013 DRIEMS ISSN (Print) : 2322-0031 , Vol. 5, Issue 1, 2017 VIBRATION ANALYSIS OF A CRACKED TIMOSHENKO BEAM USING FINITE ELEMENT METHOD Alok Ranjan Biswal*, Deepak Ranjan Biswal, Sarat Kumar Mishra * Corresponding author: alokbiswal82@gmail.com Abstract: The present day structures and machineries are designed based on maximum strength, longer life, minimum weight and low cost etc., which allow development of a high level of stresses in them which further leads to the development of crack in their elements. Many engineering structures may have structural defects such as cracks due to long-term service, mechanical vibrations, applied cyclic loads etc. So it is very much essential to know property of structures and response of such structures in various cases. The presence of crack in a structure causes a local variation in the stiffness which affects the mechanical behaviour of the entire structure to a considerable extent. Due to the existence of such cracks the frequencies of natural vibration, amplitudes of forced vibration, and areas of dynamic stability change. In order to identify the magnitude and location of the crack, analysis of these changes is essential. The information from the analysis enables one to determine the degree of sustainability of the structural element and the whole structure. Generally for the observation proposes the beam is modeled by two types. Euler-Bernoulli’s beam model where only translation mass & bending stiffness have been considered and Timoshenko beam model where both the rotary inertia and transverse shear deformation have been considered. In this paper, the presence of transverse and open crack in the Timoshenko beam has been considered and natural frequencies and mode shapes of the cracked Timoshenko beam have been studied by using finite element method (FEM) and MATLAB programme. Keywords: Crack; Timoshenko beam ;Natural Frequency;Mode Shapes;Finite element method 1. Introduction For the last several years, extensive research work has been commenced to investigate the faults in structures. It has been observed that most of the structural members fail due to the presence of cracks. Beams are one of the most commonly used elements in structures and machines, and fatigue cracks are the main cause of beams failure. The effect of crack on the dynamic behaviour of the structural elements has been the subject of several investigations for the last few decades. Papadopoulos and Dimarogonas [1] revealed the introduction of local flexibility due to presence of transverse crack in a structural member whose dimension depends on the no of degrees of freedom considered. It has been observed that the local flexibility matrix is mainly appropriate for the analysis of a cracked beam if one employs an analytical method by solving the differential equations piece wisely [2]. It is also appropriate to use a semi-analytical method by using the modified Fourier series [3, 4] and mechanical impedance method [5]. Direct and perturbative solutions for the natural frequencies for bending vibrations of cracked Timoshenko beams are provided by Loyaa [6]. Dynamic stiffness method [7], direct and inverse methods on free vibration of simply supported beams with a crack was derived by Hai-Ping Lin [8]. Crack localization and sizing in a beam from the free and forced response measurements method is indicated by Karthikeyan et al. [9].Identification of cracking in beam structures using Timoshenko and Euler beam formulation has been studied by Swamidas et al. [10]. In their work Timoshenko and Euler beam formulations have been used to estimate the influence of crack size and location on natural frequencies of cracked beam. Frequency contour method has been used to identify the crack size and location properly. Ali et al. [11] have studied the free vibration analysis of a cantilever beam. They have observed that the presence of crack in the beam, affects the natural frequency. The magnitude for the change of natural frequency depends on the change of number, depth and location of the crack. Also the change of dynamic property effects on stiffness and dynamic behaviour. The lowest four natural frequencies of the cracked structure have developed by Shin et al. [12] by using finite element method. They have obtained the approximate crack location by using Armon's Rank-ordering method that uses the above four natural frequencies. A method for shaft crack detection have