Two Algorithms for Mass Normalizing Mode Shapes From Impact Excited Continuous-Scan Laser Doppler Vibrometry

Abstract

Continuous-scan laser Doppler vibrometry (CSLDV), a concept where a vibrometer measures the motion of a structure as the laser measurement point sweeps over the structure, has proven to be an effective method for rapidly obtaining mode shape measurements with very high spatial detail using a completely non-contact approach. Existing CSLDV methods obtain only the operating shapes or arbitrarily scaled modes of a structure, but the mass-normalized modes are sought in many applications; for example, when the experimental modal model is to be used for substructuring predictions or to predict the effect of structural modifications. This paper extends an approach based on impact excitation and CSLDV, presenting a new least squares algorithm that can be used to estimate the mass-normalized modes of a structure from CSLDV measurements. Two formulations are derived: one based on real-modes that is appropriate when the structure is proportionally damped and a second that accommodates a complex-mode description. The latter approach also gives the algorithm further latitude to accommodate time-synchronization errors in the data acquisition system. The method is demonstrated on a free-free beam, where both CSLDV and a conventional test using an accelerometer and a roving-hammer are used to find its first seven mass normalized modes. The scale factors produced by both methods are found to agree with a tuned analytical model for the beam to within about ten percent. The results are further verified by attaching a small mass to the beam and using the model to predict the change in the structure’s natural frequencies and mode shapes due to the added mass.