High-order lumped-parameter models for foundation based on continued fraction

Two new types of high-order lumped-parameter models(LPMs) for foundation vibrations are proposed.The parameters of LPMs are obtained by comparing the continued-fraction dynamic-stiffness equations of new LPMs with the continued-fraction expansions of a rational function in complex frequency approximating foundation frequency response.Compared with the existing high-order LPMs,the proposed LPMs are easier to extend to high orders,and their physical configurations are condensed and independent of the problem analyzed.Moreover,due to the dynamic equations of LPMs with second-order derivative terms in time,the resulting structure-foundation-soil system can be solved by an explicit time-integration method.The effectiveness of the proposed LPMs is verified by analyzing the benchmark problem of semi-infinite rod on an elastic foundation and comparing with the results of Wu-Lee LPMs.