Optimal design of a piezoelectric smart structure for noise control

The optimal design of a piezoelectric smart structure featuring a piezoelectric actuator, sensor and a simple controller is studied to reduce the radiated sound from the structure. The structure consists of a rectangular plate on which the disk shaped piezoelectric actuator and sensor are mounted, and a negative feedback controller that returns the sensor signal to the actuator. When the structure is excited by an acoustic pressure field produced by a noise source located below the plate, sound radiates from the structure into the open space above the structure. Finite element modeling is used to model the piezoelectric structure, which incorporates a combination of three dimensional piezoelectric, flat shell and transition elements. The objective function in the optimization procedure is to minimize the sound energy radiated onto a hemispherical surface of given radius and the design parameters are the locations and sizes of the piezoelectric actuator and sensor as well as the negative feedback gain. The closed loop is constructed in the finite element equations by constraining the sensor signal and actuator signal with a negative feedback gain. The numerical result of the optimal design at a resonance frequency shows remarkable noise reduction. The optimal locations of the actuator and sensor are found to be close to the edges of the plate structure and the optimum values of the sensor and actuator sizes are increased from the initial values. The optimized results are robust such that when the acoustic pressure loading is changed, the radiated sound reduction is still maintained. At an off-resonance frequency, the same optimal design attempt was made and the optimal locations of the actuator and sensor are found to be close to the corners. Some recommendations to achieve better reduction for the off-resonance case are made.