Finite element analysis of acoustically radiating structures with applications to sonar transducers

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Abstract
A numerical technique for mathematically modeling the vibrational response of a complex structure immersed in an infinite acoustic medium is presented. The elastic response of the structure is modeled using the finite element method, and the acoustic radiation loading on the structure is modeled by approximating the surface Helmholtz integral equation formulation of the acoustic radiation problem. Arbitrary (and distinct) nodal point distributions and interpolation functions can be used in the finite element and acoustic radiation models. A technique defined in terms of these nodes and interpolation functions is presented for combining the results of these models into a combined equation of motion for the acoustically damped structure. The application of this technique to sonar transducers is discussed, including the modeling of piezoelectric material. The problem of obtaining reliable piezoelectric material parameters is discussed. Mathematical models are given for a piezoelectric sphere, a piezoelectric free-flooded cylinder, and a coaxial array of two cylinders. In general, comparison of numerical and experimental results (electric impedance plot, transmitting voltage response, beam patterns) for these devices agree within 5%. Results for the coaxial array exhibit somewhat more error.

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