Stability and identification for rational approximation of frequency response function of unbounded soil

✍ Scribed by Xiuli Du; Mi Zhao

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 298 KB
• Volume: 39
• Category: Article
• ISSN: 0098-8847
• DOI: 10.1002/eqe.936

✦ Synopsis

Abstract

Exact representation of unbounded soil contains the single output–single input relationship between force and displacement in the physical or transformed space. This relationship is a global convolution integral in the time domain. Rational approximation to its frequency response function (frequency‐domain convolution kernel) in the frequency domain, which is then realized into the time domain as a lumped‐parameter model or recursive formula, is an effective method to obtain the temporally local representation of unbounded soil. Stability and identification for the rational approximation are studied in this paper. A necessary and sufficient stability condition is presented based on the stability theory of linear system. A parameter identification method is further developed by directly solving a nonlinear least‐squares fitting problem using the hybrid genetic‐simplex optimization algorithm, in which the proposed stability condition as constraint is enforced by the penalty function method. The stability is thus guaranteed a priori. The infrequent and undesirable resonance phenomenon in stable system is also discussed. The proposed stability condition and identification method are verified by several dynamic soil–structure‐interaction examples. Copyright © 2009 John Wiley & Sons, Ltd.