Theoretical and experimental studies of an effective active vibration control method based on the deflection shape theory and optimal algorithm

Similar to mode shapes, deflection shapes are distributions of vibration amplitudes on structures under non-resonant excitations. Therefore, they are also essential vibration characteristics of structures. This paper proposes an effective active vibration control method under both nonresonant and resonant excitations based on the deflection shape theory and optimal algorithm. Taking the vibration isolation of an object on a flat plate as an example, the active vibration control method is illustrated. Piezoelectric patches are used as sensors and actuators. The main idea of the present vibration control method is to construct the suitable deflection shapes according to the position of the object by using the genetic algorithm (GA). There are two methods to select the desired deflection shapes. Under non-resonant external excitations, the desired deflection shapes are assumed artificially based on the idea of mode localization. While under resonant excitations, the desired deflection shape will be determined by the concept of destructive interference, that is, it should be completely opposite to the original one. In order to make the structure vibrate according to the desired deflection shape, piezoelectric materials are used to obtain the active loads or stiffness. The optimal actuating voltages and feedback control gains in the active control will be determined by GA. The effects of these active vibration control methods are investigated through the theoretical analyses, numerical simulations, as well as experimental verifications. These results demonstrate that the present active control method is effective.

Automated summary

This paper proposes an effective active vibration control method based on the deflection shape theory and optimal algorithm, which can be applied to both nonresonant and resonant excitations. The method is illustrated using the example of vibration isolation of an object on a flat plate. Genetic algorithm is used to construct suitable deflection shapes, and piezoelectric materials are used for vibration control.