Structural vibration suppression using PZT patches and higher-order saturation phenomena

Abstract

This paper presents the study of controlling steady-state vibrations of a cantilevered skew isotropic plate using higher-order saturation phenomena. PZT (lead zirconate titanate) patches are used as control actuators, and a laser vibrometer (measuring velocities) or PZT patches (measuring displacements) are used as sensors. Modal testing, finite element analysis, and a scanning laser vibrometer are used to reveal the plate's bending-torsional dynamic characteristics due to non-rectangular geometry. Results show that a mode shape can be significantly different from the corresponding operational deflection shape under the excitation of a PZT patch at the modal frequency. The control method uses linear second-order controllers coupled to the plate via different low-order nonlinear terms to establish energy bridges between the plate and controllers. Each linear second-order controller is designed to have a 1:2 or 1:3 or 1:4 internal resonance with one of the plate vibration modes and hence is able to exchange energy with the plate at or around the specific modal frequency. Because of nonlinearities and internal resonances, different orders of saturation phenomena exist and are used to suppress modal vibrations. Several nonlinear saturation controllers are designed and analyzed to show their feasibility and efficiency. Both perturbation analysis and direct numerical integration are used, and some experiments are performed to validate these saturation controllers.