Active control of finite beam volume velocity using shaped PVDF sensors

Abstract

Active control of volume velocity using shaped PVDF sensors is analytically studied for finite beam with different boundary conditions. Controlling the volume velocity of a finite beam is equivalent of controlling the far-field pressure above the center of the baffled beam. The shape of the PVDF sensor is determined in such a way that the output signal of the sensor is directly proportional to the volume velocity. A general expression of the PVDF sensor shape is obtained and is shown to depend only on the beam characteristics (material properties and boundary conditions). However, the shape of the sensor is independent of the type and frequency of excitation. This type of shaped PVDF sensors detects only contributions from the odd modes, which are the only ones without a nonzero volume velocity and also the most effective radiators. When a simply supported beam is subjected to a harmonic input force, the output signal of the shaped PVDF sensor is minimized by a control point force. The far-field radiated power, the mean-square velocity, and the radiation efficiency before and after the control are extensively studied. The results demonstrate that such shaped PVDF sensors are effective to control the sound radiation from the most efficient radiating flexural modes.