Stability and Identification for Continuous-Time Rational Approximation of Foundation Frequency Response

Abstract eng:
Discrete-time rational approximation (DRA) of foundation frequency response is the first step of a systematic procedure for constructing various time-domain recursive evaluations (TDREs) in foundation vibration analysis. The stability and accuracy of DRA determine those of its TDREs as realization. In this paper, the stability and identification of DRA are studied. The DRA can be obtained from a continuous-time rational approximation (CRA) of foundation frequency response. If letting the discrete-time frequency equal to the continuous-time one, the high-frequency loss and the aliasing may occur due to the periodic nature of DRA. To avoid these, the bilinear transform is used in this paper, so that the stability and accuracy of the resulting DRA is identical with those of CRA. The stability conditions of DRA are stated in z-plane. The resulting DRA is realized as the direct-form and parallel-form TDREs. The effectiveness of bilinear transform method is verified by analyzing several typical foundation vibration problems using the resulting TDREs and comparing with the results of lumped-parameter models (LPMs) resulting from the same CRA.

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