Damage Detection of Dynamic Mechanical Structures Using Modal Analysis

During the past few decades, a significant amount of research has been conducted in the area of non-destructive damage evaluation (NDE) based on changes in dynamic properties of a structure. System Identification and damage detection plays a crucial role in structural dynamics and vibro-acoustic system optimization. The later approach is based on the ‘Modal Analysis” The dynamic behaviors of the mechanical structures is typically done using a linear system modeling approach. The eigen modes of the system model can be easily visualized and direct physical interpretation can be made for the structures. A strong interest has developed with in past several years in the dynamic behaviors of machine tools and their damage detection. Vibration monitoring as a means of detecting crack initiation has been receiving much interest in recent years. This is due to the fact that it can be carried out without dismantling any part of the machine and usually even taking machine out of use, which is ultimately reducing the non-productive times of the machines. Finite element analysis is the premier analytical tool for predicting static and dynamic responses of mechanical structures. Vibrating beams are most frequently modeled using eulers Bernoulli model of beam both because of its simplicity and because it is well established an accurate approximation to real motion. In the present paper the system under consideration is assumed to be timoshenko beam, which is the simplified version of eulers beam where the shear deformations are neglected. Galerkin method is adopted for finite element formulation of the timoshenko beam. Modal parameters are obtained for cracked and un-cracked beams. The vibrational characteristics of the cracked timoshenko beam are investigated Analytical expressions and derived curves relating to the cracked depth and location on the shaft to changes in the few natural frequencies of the beam are presented. The changes in the first three natural frequencies relating to the uncracked shaft are sufficient to estimate the crack depth and crack location in the beam. Numerical examples are presented to validate the damage detection process. The results obtained help itself in damage detection of structures and for obtaining adequate system models to perform trouble shooting as well as system optimization in terms of mission critical functional performances parameters such as safety, stability, fatigue life, vibration comfort, interior and exterior noise etc.