Active control of sound radiation from a simply supported beam: Influence of bending near-field waves

Active control of sound radiation from a baffled simply supported finite beam is analytically studied. The beam is subjected to a harmonic input force and the resulting acoustic field is minimized by applying a control point force. For a single frequency, the flexural response of the beam subject to the input and control forces is expressed in terms of flexural waves of both propagating and near-field types. The optimal control force complex amplitude is derived by minimizing the acoustic radiated pressure at one point located in the far field. The far-field radiated pressure, the displacement of the vibrating beam, and the one-dimensional wave-number spectrum of the beam velocity are extensively studied. In order to further understand control mechanisms, the radiated pressure due to the flexural propagating wave and the flexural near-field wave, respectively, is investigated at the minimization point before and after the control is involved. The analysis shows that, when the control is applied, the combination of the radiated pressure due to the two different types of waves (as their associated radiation is out-of-phase) at the minimization point causes the large pressure attenuation. These results demonstrate that structural near fields are important in terms of predicting performance in active control of structurally radiated sound.