Acoustic Scattering and Active Control From a Near-Surface Underwater Piezoelastic Spherical Shell Transducer

In this paper, the 3-D interaction of a time-harmonic plane-progressive incident sound wave with a bilaminate hollow sphere, composed of an outer layer of steel perfectly bonded to an inner layer of radially polarized piezoceramic material (PZT4), and submerged near a free/rigid flat boundary, is considered. The translational addition theorem for spherical wave functions along with the classical transfer matrix approach within the context of state-space formulation is employed to obtain an analytical solution for the acoustic scattering problem. When the transducer is operating in the receive mode, the frequency spectrum of voltage induced within the piezoelectric sensor layer along with the associated backscattering form functions are calculated and discussed for selected distance parameters, angles of incidence, and interface impedance conditions. Also, when the transducer is operating in the active transmission mode, the effects of latter parameters on the control voltages required for partial or complete cancellation of the reflected pressure field are investigated.