Dynamics of Cracked Viscoelastic Beam Using Operator Based Finite Element Approach

Abstract

The presence of cracks introduces local flexibilities and changes the physical characteristics of a structure which in turn alter its dynamic behaviour. Crack depth, location, orientation and number of cracks are the main parameters that greatly influence the dynamics. By and large every material may be treated as viscoelastic and most of the time material damping facilitates to suppress vibration. Thus present study concentrates to explore the dynamic analysis of damped cantilever beam with single open crack. Operator based constitutive relationship is used to develop general linear viscoelastic model. Higher order equation of motion is obtained on the basis of Euler Bernouli and Timosenko beam theory which are converted to state-space form for eien analysis. Finite element method is utilized for the anaysis where the continuum is discretized into a number of small elements. From the results obtained, it is observed that the presence of crack decreases the natural frequency of vibration. Under cracked condition, the viscoelastic Timoshenko beam tends to give lower response values compared to viscoelastic Euler-Bernoulli beam due to the effect of shear deformation.