Non-linear vibration absorbers using higher order internal resonances

This paper presents a study of controlling steady-state vibrations of a cantilevered skew aluminum plate using saturation phenomena due to higher-order internal resonances. PZT (lead zirconate titanate) patches are used as control actuators and sensors. Linear second order controllers are designed to couple with the plate via different orders of non-linear 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's vibration modes and hence is able to exchange energy with the plate around the specific modal frequency. Because of non-linearities and internal resonances, different orders of saturation phenomena exist and are used to suppress modal vibrations. Several non-linear vibration absorbers are designed based on the saturation phenomena and are analyzed to show their feasibility and efficiency. Perturbation analysis, direct numerical integration, and experiments are performed to validate these non-linear vibration absorbers. (C) 2000 Academic Press.