Damage identification of beam structures using free response shapes obtained by use of a continuously scanning laser Doppler vibrometer system

Spatially dense operating deflection shapes and mode shapes can be rapidly obtained by use of a continuously scanning laser Doppler vibrometer (CSLDV) system, which sweeps its laser spot over a vibrating structure surface. This paper introduces a new type of vibration shapes called a free response shape (FRS) that can be obtained by use of a CSLDV system, and a new damage identification methodology using FRSs is developed for beam structures. An analytical expression of FRSs of a damped beam structure is derived, and FRSs from the analytical expression compare well with those from a finite element model. In the damage identification methodology, a free-response damage index (FRDI) is proposed, and damage regions can be identified near neighborhoods with consistently high values of FRDIs associated with different modes; an auxiliary FRDI is defined to assist identification of the neighborhoods. A FRDI associated with a mode consists of differences between curvatures of FRSs associated with the mode in a number of half-scan periods of a CSLDV system and those from polynomials that fit the FRSs with properly determined orders. A convergence index is proposed to determine the proper order of a polynomial fit. One advantage of the methodology is that the FRDI does not require any baseline information of an undamaged beam structure, if it is geometrically smooth and made of materials that have no stiffness and mass discontinuities. Another advantage is that FRDIs associated with multiple modes can be obtained using free response of a beam structure measured by a CSLDV system in one scan. The number of half-scan periods for calculation of the FRDI associated with a mode can be determined by use of the short-time Fourier transform. The proposed methodology was numerically and experimentally applied to identify damage in beam structures; effects of the scan frequency of a CSLDV system on qualities of obtained FRSs were experimentally investigated.