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SUMMARYApproximate formulas are derived to evaluate in the frequency domain the dynamic impedances of a weakly anelastic medium based on its pure elastic behaviour. The correspondence principle is applied to the elastic solution of a boundary-value problem followed by the expansion of the anelastic solution in a Taylor series about the elastic state. Taking the magnitude of material damping into account (small damping) only the first two terms of the Taylor series have been used. The derivatives of first order in the expansion can be determined by the central difference approximation; this requires only the evaluation of differences between neighbouring elastic solutions.

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A numerical model of the shape optimization of a rectangular machine foundation embedded in soil when subjected to external dynamic forces and moments is presented. A sequential programming method with move limits is used to obtain the minimum weight (mass) of the block. Numerical examples are given to illustrate the application of the model which takes 3-D dynamic soil-foundation interaction into account.