Structural energy and power flow using a scanning laser Doppler vibrometer

Abstract

A three-stage Experimental Spatial Power Flow (ESPF) method which computes an experimentally derived, spatially continuous representation of the structural power in l-D and 2-D structures is presented. The three stages of the ESPF method consist of first using a scanning laser Doppler vibrometer (SLDV) to acquire spatially dense measurements of the structure's dynamic response. Second, the continuous 3-D complex-valued velocity field is solved from the laser data. Third, a spatially continuous model of the power is computed from the velocity-field model obtained in stage 2.

The results of the ESPF method were validated by using both simulated and experimental laser data. In the simulated laser data cases, the power injected into a simply supported plate computed analytically, compared to within 1.33% of the power injected as computed by the ESPF method. In the experimental validation, three methods were used to compute the power injected and extracted from a simply supported plate forced with two shakers. The three methods consisted of the ESPF method and two methods of computing the injected power using impedance head type measurements. The injected power results were compared at four different frequencies. These frequencies were 79.0 Hz, 311.0 Hz, 909.0 Hz, and 1100.0 Hz. In all cases, the injected and extracted power results of the three methods compared to within 20% and to within 12% for all cases except the 909.0 Hz case. These results are currently better than other experimental techniques.

Advantages of this method are 1) a spatially continuous representation of the power is computed 2) the affects of the actual boundary conditions and near-field effects of the structure are inherently measured by the SLDV 3) the SLDV does not affect the response of the structure by mass loading and is fully portable for in-field testing 4) the method allows for convergence of the power-flow vector field in addition to convergence of the velocity field and 5) the ESPF method is extendable to account for power due to in-plane motion and to account for shells of arbitrary geometry.