ACTIVE CONTROL OF FINITE BEAM VOLUME VELOCITY USING SHAPED PVDF SENSOR

The radiated sound power of a planar structure is related to the struc tural volume velocity in the low frequency region. The volume velocity associated with a vibration structure is also related to the far-fiel d pressure in the direction orthogonal to that structure. Thus, the mi nimization of the volume velocity appears as a good strategy for activ e control of sound radiation. This paper investigates the design of a volume velocity sensor and its integration into an active noise contro l system in the case of a flexural beam (1D structure). Based on a mod al approach, the shape of a PVDF sensor is analytically determined in such a way that the output signal of the sensor is directly proportion al to the volume velocity of a harmonically excited finite beam with a rbitrary boundary conditions. A general expression of the PVDF sensor shape is obtained and is shown to depend only on the beam and sensor c haracteristics (material characteristics and boundary conditions). The shape of the sensor is independent of the type and position of the ex citation and the control actuator considered. For simply supported or clamped boundary conditions, this type of shaped PVDF sensor detects o nly contributions from the odd (symmetric) modes, which are the only o nes with non-zero volume velocity and also the most effective radiator s. For a cantilever beam, this sensor will detect all the modes since none of them has zero volume velocity. A piezoceramic actuator is used to minimize the output signal of the shaped PVDF sensor. The efficien cy of this control strategy is demonstrated analytically for a simply- supported and cantilever beam. The far-field radiated acoustic power, the quadratic velocity as well as the radiation efficiency are extensi vely studied. The results show that such PVDF shaped sensor is very ef fective in controlling the sound radiation. Experimental implementatio n of such a PVDF volume velocity sensor as well as the active control using a feedforward harmonic adaptive LMS algorithm are presented and discussed.