Application of distributed measurements for finite element model verification
The wealth of experimental laser data and its high accuracy allow a rigorous comparison between a distributed model and distributed measurements that was not possible previously. The purpose of this work is to obtain and compare experimental and analytical distributed measurements for a simple structure excited by a point force (from a shaker) and by a distributed force (from a single or pair of piezoceramic actuators). The analytical results are obtained from the forced response analysis of a finite element model. A known piezoelectric actuator model that shows the actuation effects produced by symmetrically bonded actuators are line moments along the edges of the actuator and the effects produced by a single actuator are line moments and forces along its edges is used. A forced response analysis is performed on this model and the amplitude of the sinusoidal displacement at each prescribed point along the structure is found. Experimentally, a scanning laser vibrometer is used to measure the velocity along the structure due to the hannonic excitations. The vibration amplitudes are found from these results and compared to the modeling results. The predicted displacement shapes for the various excitations and boundary conditions resemble the measured shapes. The exact magnitudes of the predicted displacements along the beam do not corroborate the experimental results. The differences between the two are inconsistent over the length and width of the beam and over the excitation frequencies considered. Various modeling and experimental reasons are cited for this inaccuracy. The other moments from the edges of the piezoceramic actuators parallel to the length of the beam are found to influence the beam response even at low frequencies. The laser measures some torsional effects in the beam that are not predicted by the model. The measured responses show that at high excitation frequencies mode shapes indicative of a plate are excited in the beam by the piezoceramic actuators.