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Model degrees-of-freedom reduction and frequency windowing via interpolation are combined for application to acoustic finite element analysis problems. Projection operators are employed for the model reduction or condensation process. Interpolation is then introduced over a user defined frequency window, which can have real and imaginary boundaries and be quite large. Hermitian interpolation functions (which require derivative information) as well as standard Lagrangian functions, which can be linear, quadratic or cubic, have been used to construct the windows. For one-dimensional windows, the location of interior evaluation points can be varied to increase accuracy. Results are excellent for example problems, even for large d.o.f. reduction and large frequency windows containing numerous resonances (eigenvalues). The reduced models within the windows appear to indicate accurately the location of the resonances.

The polarization obtained in the direction of an arbitrary uniaxial stress is derived by applying tensor transformations to the polarization-stress relation: Pi, = dijkσjk. Two- and three-dimensional plots of the results are shown. The experimental work described includes the preparation of discs poled uniformly at 90° to their thickness and the measurement of d333 as a function of orientation. Very good agreement with the calculated results was obtained. The effect of electrodes on the measurement of d333 (d33) and the use of a d311 (d31) parameter measurement to permit a d113 (d15) determination are also demonstrated. The d333 measurements as a function of stress orientation permitted determination of the d15 value with a resolution of ±8%. Its average value was within 5% of d15 values derived from other techniques.

The Retarded Potential (RP) method, which is a boundary element technique and non-local in both space and time, is employed to discretize the fluid domain for the analysis of transient fluid–structure interaction problems. The retarded potential analysis program RPFS is coupled to the ABAQUS non-linear finite element code to form ABAQUS/RPFS. The standard RP is inherently unstable for time steps below a critical time step that is equal to the maximum distance in the fluid divided by the wave speed. A technique referred to as the Figueiredo method is used to convert the standard RP differential-delay equations for the fluid to simply delay equations, which are more stable. The Figueiredo approach extends the stability range of the standard RP by a factor of approximately 10–20, but this time step is still not small enough to be useful for analysis. Digital signal processing methods are used to further stablize the response of the fluid by removing the oscillating high-frequency noise in the time histories of the solution without introducing phase shifting or any significant damping. Stability of the coupled system is achieved by not extrapolating the structural accelerations. ABAQUS/RPFS is applied to both a rigid and elastic sphere subjected to a plane wave, and the results using the full time histories required are completely stable and quite accurate. With this procedure, the retarded potential method may yet prove to be a valuable analysis tool for transient fluid–structure interaction problems. © 1997 John Wiley & Sons, Ltd.