Active sound radiation control of a submerged piezocomposite hollow sphere

Abstract

A spatial state-space approach based on the linear three-dimensional exact piezoelasticity theory along with the Helmholtz equations for the internal/external acoustic domains are employed to describe the coupled vibroacoustic response of an arbitrarily thick, spherically isotropic, functionally graded, radially polarized piezolaminated hollow sphere, immersed in and filled with ideal compressible fluids, and under the actions of arbitrary (non-axisymmetric) distributed time-harmonic transverse mechanical excitations at its inner and/or outer boundaries. A frequency domain subspace–based identification technique is applied to estimate the coupled fluid-structure dynamics of the system in the controller design stage. Subsequently, a standard linear quadratic Gaussian optimal controller is synthesized and simulated based on the identified model, and the optimal control input voltages for suppressing the sensor output voltage (total radiated power) of the submerged sphere are calculated for selected weighting parameters associated with the system response and control input. Numerical simulations establish the effectiveness of the selected (partial/full) sensor/actuator configuration in conjunction with the adopted control strategy for attenuating the predicted sound radiation response of an air-filled, water-submerged, sandwich piezocomposite (PZT4/steel/PZT4) sphere, in both frequency and time domains. Also, the trade-off between dynamic performance and control effort penalty is examined for impulsive and Gaussian random external mechanical disturbances. Furthermore, the effect of piezoelectric material gradient variation on sound radiation control performance of the smart piezocomposite structure is briefly discussed. The validity of the acousto-elastic model is demonstrated by use of a commercial finite element package as well as by comparison with the data available in the literature.