Power mode shapes for early damage detection in linear structures

Establishing non-modal-based damage indices for non-destructive damage detection purposes, using the statistical properties of signals is a worthwhile topic and so far little literature related to this aspect can be found. As an alternative to the conventional mode shape, a new concept of power mode shape constructed using the root mean square property of response signals is proposed in this paper. Power mode shapes possess similar shapes to conventional mode shapes but are obtained by basing them on signal power spectral densities without any modal parameter extraction. In addition, two extended parameters initially named as power mode shape curvature and power flexibility are derived using power mode shapes. Damage indices are defined by using power mode shape curvature and power flexibility as two means of locating damage in different numerical and experimental structures under random excitation with the damage being indicated by prominent peaks. Satisfactory predictions are given for both single and multiple damage situations, and minor damage inducing few changes in the structural dynamic properties can also be detected, which is meaningful and important for early damage detection. The analysis results show a potential use of the proposed method for damage detection purposes. A further experimental study on real structures is an important prerequisite before the practical application.