Multimodal nonlinear damping technique using spatial filtering

A nonlinear damping strategy using spatial filtering aiming at attenuating multimodal vibrations in a flexible structure is proposed and applied to a clamped–clamped steel beam. Based on the mode shapes, four piezoelectric patches are symmetrically or antisymmetrically attached on the surfaces of the beam close to the clamped ends. To suppress odd modes, two antisymmetrically attached patches are intermittently connected to a switching device consisting of a digital switch and an inductor. The electronic switch is kept open unless the sum of the two piezovoltages reaches an extremum value. When the switch is closed, the antisymmetrically bonded patches and the inductor constitute an oscillator. The switching time corresponds to half a period of this oscillator until the sum of two piezovoltages has been reversed. In a similar way, symmetrical patches based on the difference signal are used for controlling even modes. Experimental setup for controlling the first two vibration modes of a clamped–clamped beam is established to validate the analytical results based on finite element method. Corresponding results showed that the proposed damping strategy using spatial filtering exhibits better performance and allows an effective bimodal control method without significantly increasing the complexity and can be easily extended to multimode control.