Hybrid finite element formulation for periodic piezoelectric arrays subjected to fluid loading

The effect of fluid loading on a structure embedded with a periodic distribution of piezoelectric transducers is considered in a hybrid formulation that involves a finite element formulation for the structure and transducers that is coupled to an analytical series representation of the acoustic field in the fluid. The passive fluid loading redefines the stiffness matrix via a radiation impedance term. Modal analysis of the array can be effected for elastic vibrations, open and close circuited electrical boundary conditions. General damping in the stiffness as well as dielectric constants is considered. Sensor and actuator equations are then formulated. The actuator equations permit computation of the displacement and stress distribution in the transducer and structure when a known voltage is applied to the transducer electrodes. The sensor equation is illustrated for the case of a known incident plane harmonic wave obliquely incident on the array. The voltage induced in the transducer elements can then be computed.