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 zirconate titanate) patches. Finite-element analysis and measurement of operational 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 controllers coupled to the plate via quadratic terms to establish energy bridges between the plate and controllers. Each linear second-order controller is designed to have a 1:2 internal resonance with one of the plate vibration modes and hence is able to exchange energy with the plate around the corresponding modal frequency. Because of quadratic nonlinearities and 1:2 internal resonances, saturation phenomena exist and are used to suppress modal vibrations. To test this saturation control technique in an efficient and systematic way, we built a digital control system that consists of SIMULINK modeling software and a dSPACE DS1102 controller in a personal computer. Both numerical 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 regulate dynamics of structures to prevent resonant vibrations by designing each controller to control one vibration mode.