Finite Element Based Vibration Analysis of a Nonprismatic Timoshenko Beam with Transverse Open Crack

Abstract

The present day structures and machineries are designed based on optimizing of multiobjectives such as maximum strength, maximum life, minimum weight and minimum cost. Due to this they are flexible and allow having a very high level of stresses. This leads to development of cracks in their elements. Many engineering structures may have structural defects such as cracks due to long-term service. So it is very much essential to know the property of structures and response of such structures in various cases. The present article deals with finite element based vibration analysis of a cracked beam. The beam is modeled using the Timoshenko beam theory. The governing equation of motion has been derived by the Hamilton’s principle. In order to solve the governing equation two noded beam element with two degrees of freedom (DOF) per node has been considered. In this work the effect of structural damping has also been incorporated in the finite element model. The analysis is carried out by using state space model in time domain.