Applications of Distributed Piezoelectric Electrode Patches for Active Noise and Vibration Control

Abstract

In the present contribution the concept of dynamic shape control is applied to compensate disturbing vibrations in a composite structure. Particularly, a three-layer cantilever beam is investigated as a representative example, where displacements due to a superimposed support motion are compensated by means of two piezoelectric actuator layers. In a first step, it is assumed that the piezoelectric actuation can be applied continuously along the actuating layers of structure. As an analytic solution it follows that the deflections can be compensated all over the beam at every time instant, if the piezoelectric actuating moment coincides with a quasi static bending moment due to the rigid body parts of the inertia forces that are produced by the support motion. This solution afterwards is realized by using discrete electrode patches attached to the continuous piezoelectric actuator layers. The amount of electrical voltage applied to the discrete electrode patches is chosen such that the area under the analytical solution curve is equalized. Mohr’s analogy for the computation of beam deflections is used in order to show that this equal-area rule enforces the slope of the displacement curve to vanish at several places of the beam in a quasi static sense. In a further step, we apply the electric voltages derived from the equal-area rule of beam theory to a refined model of the composite beam derived by means of the Finite Element method. A harmonic resonant motion of the cantilever is considered, driving the beam into resonant vibrations. The cantilever is modeled by means of plane-stress Finite Elements, taking into account electromechanical coupling. In this numerical study, the goal of shape control is reached with a high accuracy. This gives excellent evidence for the usefulness of the proposed method of shape control by discrete electrode patches also for active control.