基于Chebyshev复多项分式的地基集总参数模型研究  

LUMPED-PARAMETER MODELS FOR FOUNDATIONS BASE ON CHEVSHEV COMPLEX POLYNOMIALS-FRACTION

作　　者：王海[1] 刘伟庆[1] 王曙光[1] 杜东升[1] 李昌平[1] 

机构地区：[1]南京工业大学土木工程学院,南京210009

出　　处：《工程力学》2013年第3期133-139,151,共8页Engineering Mechanics

基　　金：国家自然科学基金重大研究计划项目(90815017);土木工程防灾国家重点实验室开放课题基金项目(SLDRCE10-MB-06)

摘　　要：该文基于改进的Chebyshev复多项分式在复数拟合中的应用,给出了各种基础(表面圆形基础、埋置方形基础、桩基础)阻抗函数的集总参数模型。该文使用改进的Chebyshev复多项式的比值表示地基的动力柔度函数,通过定义误差函数,使用最小二乘法得到改进的Chebyshev复多项式的系数。然后将改进的Chebyshev复多项分式表示成部分分式的形式并将其等效为两种基本类型的弹簧-阻尼器模型。通过与地基动力刚度阻抗函数的弹性半空间解进行比较,该文使用的Chebyshev复多项式在阶数很小时,得到的集总参数模型即能在很宽的频段上反映精确解的变化。该文模型可以在时域和非线性分析中使用。This paper puts its attention on the application of Chebyshev complex polynomials in the development of an extensible lumped-parameter model of unbounded soil. The normalized flexibility function of foundations is adopted to improve the accuracy of the model and to reduce the parameters in modeling. A ratio of two Chebyshev complex polynomials is adopted to represent the normalized flexibility function of foundations. Through performing a partial-fraction expansion on this Chebyshev complex polynomial-fraction, a Chebyshev complex polynomial-fraction is designed as two basic discrete-element models. The accuracy and validity of the lumped-parameter model are extensively investigated for the case of foundations. Subsequently, these models are applied for representing the dynamic stiffness functions of foundations. The proposed method may be easily applied to analyze various practical problems in soil-structure interactions in a time domain and nonlinear analyses.

关 键 词：集总参数模型 地基柔度函数 土-结构相互作用 Chebyshev复多项式 非线性分析 

分 类 号：TU470[建筑科学—结构工程] TU973.35[建筑科学—土工工程]