Active sound radiation control of a thick piezolaminated smart rectangular plate

A spatial state-space formulation based on the linear three-dimensional piezoelasticity theory in conjunction with the classical Rayleigh integral acoustic radiation model is employed to obtain a semi-analytic solution for the coupled vibroacoustic response of a simply supported, arbitrarily thick, piezolaminated rectangular plate, set in an infinite rigid baffle. The smart structure is composed of an orthotropic supporting core layer integrated with matched volume velocity spatially distributed piezoelectric sensor and uniform force actuator layers. To assist controller design, a frequency-domain subspace-based identification technique is applied to estimate the coupled fluid–structure dynamics of the system. A standard linear quadratic Gaussian (LQG) optimal controller is subsequently synthesized and simulated based on the identified model and the optimal control input voltage for minimizing the estimated net volume velocity (total radiated power) of the panel is calculated in both frequency and time domains. Numerical simulations demonstrate the effectiveness of the adopted volumetric sensing/actuation technique in conjunction with the optimal control strategy for suppressing the predicted sound radiation response of a three-layered ( Ba 2 NaNb 5 O 15 / Al / PZT4 ) sandwich panel in both frequency and time domains. The trade-off between dynamic performance and control effort penalty is examined for two different types of loading (i.e., impulsive and broadband random disturbances). Validity of the results is demonstrated by comparison with a commercial finite element package, as well as with the data available in the literature.