Panel with self-tuning shunted piezoelectric patches for broadband flexural vibration control

A practical approach based on maximisation of vibration power dissipation is proposed for the self-tuning of single- and multi-resonant shunts connected to piezoelectric patches, which are bonded on thin rectangular panels to reduce the broadband flexural vibrations produced by stochastic disturbances at low audio-frequencies. The single- and multiresonant shunts are formed either by one or by multiple resistance-inductance-capacitance (RLC) branches connected in parallel. The proposed self-tuning approach sequentially adapts the RL elements in the branches of each shunt in such a way as to maximise the vibration power dissipation from the resonant response of the flexural modes of the hosting structure that resonate in a target frequency band. The vibration power dissipated is estimated from the measured electric power dissipated by each shunt so that self-tuning can be implemented locally and independently in each shunt without the need of system identification or on-line measurement of the vibration response of the hosting structure. Therefore, on-line tuning can be implemented to control the vibrations of distributed structures, also in those cases where they are characterised by time-varying dynamics, generated, for example, by tensioning effects, mass variations, moving loads, uneven constraints, etc. To start with, the paper presents a parametric study on a thin rectangular panel with two piezoelectric patches connected to multi-resonant shunts, which shows that, the time-averaged total flexural kinetic energy of the smart panel and the timeaveraged electric power dissipated by each shunt are characterised by matching local minima and maxima, which identify the optimal RL parameters in the branches of each shunt necessary to control the resonant responses of the panel low order flexural modes. A practical iterative approach, based on the maximisation of the time-averaged electric power dissipated by each shunt, is then introduced to find on-line these optimal RL parameters. Finally, a brief survey is presented to show the flexural vibration control effects produced in the panel by increasingly larger arrays of piezoelectric patches connected to the proposed self-tuning multi-resonant shunts.