Active vibration control of a plate using vibration gradients

Abstract

Minimization of the squared transverse velocity at a measurement point does not guarantee the global vibration reduction for the whole structure, and the control result is dependent on the measurement point. Flexibility of the sensor placement is usually limited in practice. If the measurement point is near the nodal line of the mode, this mode cannot be decreased effectively and even increased by the control force. This study investigates the control method with the error criterion being the sum of the squared vibration velocity and the squared vibration gradients (spatial gradients) at a measurement point. Since the spatial distributions of the vibration velocity and its gradients are different, the aforementioned problem caused by the nodal line are mitigated. The numerical examples indicate that the performance of the control including the vibration gradients is less dependent on the measurement point, and this method achieves a better global vibration reduction, than the conventional method, i.e., minimization of the squared vibration velocity.