Finite element modeling of a piezoelectric smart structure for the cabin noise problem

Abstract

Finite element modeling is used to study the response of a piezoelectric smart structure for the cabin noise problem. One side of a cubic-shaped cavity is covered with a flat plate on which a disk-shaped piezoelectric actuator and sensor are mounted, and a plane wave noise is impinging on the plate. The sensor signal is returned to the actuator via a negative gain such that it can reduce the noise at a certain zone in the cavity. The finite element method which uses a combination of three-dimensional piezoelectric, flat shell and transition finite elements is adopted to model the piezoelectric smart structure. To take into account the acoustic pressure in the cavity, the modal approach is used and by invoking the orthogonality of the mode shapes in the cavity, the interaction force on the structure caused by the pressure is included in the finite element equations. Without any activation, the pressure field at a point in the cavity is investigated according to the excitation frequency. To prove the validity of the proposed finite element approach, a comparison is made with a commercial elasto-acoustic analysis package and it shows a good agreement. Thus, the proposed approach is found to be useful to model piezoelectric smart structures for cabin noise problems. A major advantage of this method is that it can reduce the size of the system equation by eliminating the acoustic pressure terms, which gives a computational economy. The finite element modeling is tested for active systems. When the sensor signal is returned to the actuator with some gain the average pressure at a point in the cavity is remarkably reduced. To confirm the usefulness of piezoelectric smart structures for active cabin noise control, intensive studies regarding the size and locations of actuator and sensor as well as the gain are necessary.