Rotational Flexibility for Detecting Low Level Damage in Beam-Like Structures

Abstract

This paper proposes a methodology for damage detection in beam like structures using vibration characteristics obtained from transfer matrix technique. At first, vibration characteristics of beam-like structure have been determined with the help of a computer program developed based on the formulations presented in this paper. Then, a detailed study has been carried out to categorise the influ- ence of damage on frequency and mode shape (both displacement and rotational) information. For a structure with known magnitude and location of damage(s), frequencies and mode shape information are obtained and the same has been used in determining the damage in the structure. It is observed that the change in fre- quency with damage is very small but it is easy to measure. Mode shape infor- mation is very sensitive to damage but it is prone to experimental errors. Hence, a methodology for damage detection, specifically for low level of multi-damage cases, has been proposed using both frequency and rotational mode shape informa- tion obtained from a damaged structure. Curvature of rotational flexibility has been proposed and demonstrated to be an improved indicator of damage than the estab- lished ones. Further, uniform moment surface has been developed by incorporating number of lower mode information to reduce the error from any particular mode. The proposed damage indicator is enhanced by Chebyshev polynomials for better performance. It is observed that the proposed damage indicator is capable of iden- tifying locations of damage in structure even for case of very low damage. Here, no prior knowledge or information on the undamaged (intact) stage of the structure is required for this proposed methodology. Hence, the methodology presented here provides a simple and efficient tool for detection and localisation of damage(s) in distressed structure.