Dynamics regulation of a skew cantilever plate using PZT patches and saturation phenomenon

We investigate the suppression of steady-state vibrations of a cantilevered skew aluminum plate using nonlinear saturation phenomena and PZT (lead zir conate titanate) patches. Finite-element analysis and measurement of operat ional deflection shapes using a scanning laser vibrometer are performed to study the bending-torsional dynamic characteristics of the plate due to non -rectangular geometry. The control method uses linear second-order controll ers coupled to the plate via quadratic terms to establish energy bridges be tween the plate and controllers. Each linear second-order controller is des igned to have a 1 :2 internal resonance with one of the plate vibration mod es and hence is able to exchange energy with the plate around the correspon ding modal frequency. Because of quadratic nonlinearities and 1:2 internal resonances, saturation phenomena exist and are used to suppress modal vibra tions. To test this saturation control technique in an efficient and system atic way, we built a digital control system that consists of SIMULINK model ing software and a dSPACE DS1102 controller in a personal computer. Both nu merical and experimental results show that this nonlinear control method is robust in suppressing steady-state resonant vibrations without significant spill-over effects. Hence the saturation controllers can be used to regula te dynamics of structures to prevent resonant vibrations by designing each controller to control one vibration mode.