Transfer Functions to Measure Translational and Rotational Velocities with Continuous-Scan Laser Doppler Vibrometry

Matthew S. Allen Assistant Professor [email protected] Department of Engineering Physics University of Wisconsin-Madison 535 Engineering Research Building 1500 Engineering Drive Madison, WI 53706 Abstract A laser Doppler vibrometer typically measures the translational velocity at a single point along the direction of incident light. However, it has been shown that rotational velocities can also be recovered by scanning the laser continuously along a line or circular path around that point. This work uses the harmonic transfer function concept, which is analogous to the transfer function in conventional modal analysis, to relate the measured rotational and translational velocities to the input force. With this concept, the continuous-scan approach can be combined with the conventional point by point scan approach, acquiring normalized translational and rotational 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 measurements taken from a downhill ski under free-free boundary conditions. The influence of the circle size, the scanning rate and the surface quality on the noise level in the measured signal is discussed, and the measured deflection shapes using both the point and circular scan approaches are compared. Local slopes at measurement locations are computed from the identified principal rotational velocities, laying the foundation for constructing a much more accurate estimate of the deformation shape, which may be valuable in damage detection and/or model updating.