A design method for achieving weak radiator structures using active vibration control

Abstract

A general strategy is devised for achieving minimum radiation of sound from structures subjected to a harmonic excitation force. A quadratic expression is written for the total sound power radiated from a structure in terms of the primary excitation and actuator (control) forces. Using quadratic optimization of this expression, a single control force vector is found that minimizes the radiated sound power (weak radiator). A general formulation is presented for the single-frequency excitation case. This formulation is then extended to the case of a structure subjected to a broadband excitation force; i.e., the magnitude and the phase of the excitation force remain constant as the excitation frequency changes. The numerical implementation of these formulations is described for a baffled beam controlled by forces and moments generated by piezoelectric actuators. Results for a single-frequency weak radiator show that the radiation efficiency of the beam response with control is drastically lower than that of the beam response with no control. Also, when the response of the structure with control is compared to that of the structure without control, three important observations can be made. First, the controlled structure exhibits lower response amplitudes at frequencies near structural resonances. Second, the controlled structural response amplitude decreases near the boundaries. Third, the wave number content of the controlled structural response shifts from supersonic to subsonic regions. These observations are confirmed experimentally using a clamped–clamped beam excited at a single frequency with a shaker and four PZT actuators bonded to its surface.