Creating bandgaps in active piezoelectric slender beams through positive position feedback control

Abstract

Bandgaps—frequency ranges with reduced vibration transmissibility in elastic structures, are an opportunity for vibration control originating from the research on elastic metamaterials. In this paper, we study the design for bandgap in slender beams with collocated piezoelectric patch transducers. While creating bandgaps using shunted transducers is a well-established research field, using structures with piezoelectric sensors, actuators, and feedback controllers for the same application has not been thoroughly explored. This paper aims to study the use of the tools originating from the active vibration control (AVC) field for bandgap generation in finite beams with collocated piezoelectric sensors and actuators. Lightly damped second-order low-pass filters are used as controllers in the same configuration as positive position feedback, widely used for active damping. To facilitate the understanding of systems behaviour, we propose a simplified model based on the Euler–Bernoulli beam theory. A modal analysis approach and an assumption of an infinite number of transducers of infinitesimal length distributed along the structure are used to predict the frequency range of the locally resonant bandgap in closed form. The experimental part of the work demonstrates the feasibility of the proposed approach for creating bandgaps in practice. Thanks to the insights from AVC, the control system can be designed purely based on experimental frequency response data without the need for a parametric model of the system. We also show that the uniform distribution of actuators is not necessary for creating bandgap, which can be achieved in a structure with a relatively small number of sparsely placed actuators and compare the obtained results with analytical predictions for ideal metastructure. Low-frequency bandgaps placed between 10 and 320 Hz are obtained in experiments.