Piezoelectric transducers for broadband vibration control

This thesis presents theoretical and experimental studies concerning active and semi-active systems for the vibration control of the flexural response of a thin plate using piezoelectric transducers. Concerning the active control systems, velocity feedback loops are implemented using a piezoelectric patch with a particular shape as actuator. This piezoelectric patch is composed of 6 triangular leafs disposed in such a way as to form an hexagonal patch. Single and decentralised multiple channel configurations were studied, using the Nyquist criteria to analyse the stability of the control loop and the kinetic energy of the flexural response of the panel to asses the control performance. Then, a fully coupled model of a semi-active vibration control system is presented, which uses a piezoelectric transducer connected to an electric shunt circuit composed of an inductance and a resistance. A reduced model that neglects the structural damping and considers only the first natural mode of the plate was used to derive the optimum values for the inductance and resistance of the shunt circuit. These values were then compared to the ones found numerically using a genetic algorithm and considering an increasing amount of natural modes of the plate. A parametric study is also presented in which the effects of the piezoelectric patch dimension on the vibration control performance is analysed. The last part of the thesis presents a time-varying shunted piezoelectric absorber that produces a broadband control effect of the flexural response of the plate. Single and multiple configurations were studied, and two control laws were proposed for the shunt: switching mode, in which the inductance and resistance values cyclically change between a set of three pairs of values in order to control iteratively the flexural response of the panel near three of its natural frequencies; and sweeping mode, in which the shunt values are varied continuously from a lower to an upper bound that match the lower and upper values of the frequency range of interest. Series and parallel operation modes are proposed for the multiple configuration using five time-varying shunted piezoelectric vibration absorbers. In the series mode the targeted frequency range is divided in five sub-ranges in which only one piezoelectric vibration absorber works and in the parallel mode all five absorbers work in the full targeted frequency range but with a phase shift between each other.