Effective Placement of a Cantilever Resonator on Flexible Primary Structure for Vibration Control Applications—Part 2: Model Updating and Experimental Validation

In this Part 2 of a two-part series, the experimental verification and comparison of this work are presented. In this paper, the effect of beam-type resonator position on flexible dynamics is determined experimentally. The system is excited using band-limited white noise via electrodynamic shaker, and the data are collected with several transducers and a high-speed camera for each actuator beam mounting location; the first four mode shapes and natural frequencies are determined, and a finite element model (FEM) is developed and updated using these data. An additional set of data is collected using a linear sine chirp forcing function and the updated/experimental frequency response functions (FRFs) and time responses for the base and actuator beam tips are found to correlate. Plots of experimentally determined percent modal strain energy versus attachment position for the first four modes is presented, and a final study is also performed showing the fractional root-mean-square (RMS) strain energy in the actuator with respect to the total system. A final set of data is collected in which the actuator beam is moved up the base beam, the piezoelectric patch of the actuator beam is energized with white noise, and the tip response of the base beam is measured; an RMS base beam velocity versus mount position plot was developed. From this work, it is determined that the most practical/optimal position for the secondary beam to serve as both a sensor and actuator to control base beam tip response over a wide frequency band is in the nondimensionalized range: $0.4≤e<0.6$⁠.