Harmonic Transfer Function to Measure Translational and Rotational Velocities With Continuous-Scan Laser Doppler Vibrometry

Abstract

A laser Doppler vibrometer measures the translational velocity at a point along the direction of incident light. It has been shown that rotational velocities can also be recovered when the laser scans continuously along a short line or small circular path around that point. This work uses the harmonic transfer function to relate the measured translational and rotational velocities to the input force. With this concept, the continuous-scan approach can be combined with the conventional point-by-point scheme, acquiring three dimensional velocities under various types of excitation conditions in the same amount of time that is required for obtaining only the translational velocity. The proposed approach is validated on a downhill ski under free-free boundary conditions with a circular scan pattern. The influence of the circle size, the scan rate and the surface quality on the noise level is evaluated. It is found that the circular-scan approach provides smoother and more reliable mode shapes than the conventional point-by-point approach given appropriate parameters. Local slopes at the measurement locations are then computed from the identified rotational velocities, providing additional information for model validation and damage detection.