Active noise control studies using the Rayleigh–Ritz method

The use of piezoelectric materials in controlling the vibration of continuous structures has grown significantly in recent years. A number of studies using Finite Element (FE) method [1, 2, 3, 4] have been made on noise transmission studies for rectangular enclosures through flexible smart panels. In these models, the host plate, actuators and sensors are modeled using 2D and 3D elements, which are later coupled, to the cavity in which the pressure is expressed in terms of rigid cavity modes. Although these earlier FE models predict the behavior of the structural panel and the fluid-structure interaction accurately at low frequencies, at high frequencies the size of the model increases resulting in very long computational time. Further, optimal sensor/actuator placement studies, involve repeated FE remeshing during the iterations, hence a simple model like the RR approach is preferred. The potential and kinetic energies of the panel with surface bonded discrete piezoelectric patches are estimated and the equations of motion for the smart panel are derived using Hamilton’s principle. The electric potential inside the piezoelectric patches are assumed to be a quadratic function of thickness coordinate. Classical laminated plate theory is used for modeling the host plate and the electroelastic theory is used to model the surface bonded patches. In electroelastic theory, reduced charge equation is satisfied inside both sensor and actuator patches. For the acoustic enclosure, the cavity pressure is expressed in terms of rigid cavity modes [5]. For the numerical study and to validate the RR approach, the frequencies obtained using RR approach are compared with the FE results for a smart aluminum plate backed cubic cavity.