Optimal placement of microphones and piezoelectric transducer actuators for far‐field sound radiation control

This paper presents an optimization solution technique to determine the optimal locations of piezoelectric transducer (PZT) actuators and far‐field microphone sensors for active structural acoustic control in conjunction with the use of least‐mean‐square (LMS) feedforward control algorithm. A simply supported beam in an infinite rigid baffle subject to an harmonically excited point force is considered. The piezoceramic patches are adhered to the beam and act as control transducers, while microphones located in the far field are used as error sensors. The objective function is first defined as the total radiated sound power. The design variables which are the locations of PZT actuators and microphone sensors are then identified and determined. The genetic algorithm (GA) incorporated with the use of linear quadratic optimal control theory (LQOCT) to calculate the control voltages to the actuators is adopted to solve the optimization problem. Results show that the optimally placed PZT actuators and microphone sensors can perform better sound radiation control than the arbitrarily selected ones. In particular, for off‐resonance excitation cases the optimized PZT actuators and microphone sensors can efficiently control the sound radiation and eliminate the control spillover. The control mechanisms of PZT actuators and microphone sensors are demonstrated through the studies of radiation directivity patterns and beam displacement distributions as well as the wave‐number analysis. The effect of the number of microphone sensors are also presented. The use of optimally positioned PZT actuators and microphone sensors can efficiently achieve structural sound radiation control.