Dynamic Response of Arbitrarily Shaped Foundations

The paper presents a method to compute the effective dynamic stiffnesses (K¯) and dashpots (C) of arbitrarily shaped, rigid surface machine foundations placed on reasonably homogeneous and deep soil deposits. The method is based on a comprehensive compilation of a number of analytical results, augmented by additional numerical studies and interpreted by means of simple physical models. All results are offered in the form of easily understood dimensionless graphs and formulae, covering the six modes of vibration and a wide range of frequencies, for both saturated and unsaturated soils. Comparisons are made with the widely used equivalent circle approximation. The proposed method is applicable to a variety of area foundation shapes, ranging from circular to strip and including rectangles of any aspect ratio as well as odd shapes differing substantially from rectangle or circle. The results confirm that both frequency and foundation shape may significantly affect K¯ and C. Insight is gained into the mechanics of radiation damping and a general conclusion is drawn regarding its magnitude at high frequencies for different foundation shapes and vibrational modes. The practical application of the method is illustrated with a specific example, while a companion paper presents supporting experimental evidence from model tests.

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