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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。
Based on the application of the modified Chebyshev complex multinomial in complex fitting, a lumped parameter model of impedance functions for various foundations (surface circular foundation, embedded square foundation and pile foundation) is presented. In this paper, we use the improved ratio of Chebyshev polynomials to represent the dynamic compliance function of foundation. By defining the error function, the coefficients of the improved Chebyshev polynomials are obtained by using the least square method. The improved Chebyshev complex multisection is then expressed as a fractional form and is equivalent to two basic types of spring-damper models. By comparing with the elastic half-space solution of impedance function of ground dynamic stiffness, the Chebyshev complex polynomial used in this paper can reflect the change of exact solution over a wide frequency band when the order is small. The model can be used in time domain and nonlinear analysis.