Modal amplitude extraction of guided waves in rails using scanning laser vibrometer measurements

It is advantageous to be able to measure the amplitude of the individual modes of propagation during the development of guided wave systems for rail monitoring. This paper addresses the problem of extracting modal amplitudes from scanning laser vibrometer measurements. The wave propagation characteristics of the rail are computed using the semi-analytical finite element method, and are used to represent the frequency response at a set of measurement locations (with unknown amplitude coefficients). Experimental frequency responses are measured and the amplitude of each mode is estimated using a pseudo-inverse technique. The selection of measurement points is investigated. A set of measureable points is defined based on accessibility and scanning angles. A technique is proposed for selecting appropriate measurement points, from within this set, to yield a well conditioned problem. It is shown that there exists a number of points, above which additional points do not add to the accuracy of the process. The method is demonstrated on a 5 m length of rail excited by a piezoelectric transducer in the lab.