| Summary: | 碩士 === 國立雲林科技大學 === 營建工程系碩士班 === 89 === Based on the approximation by polynomial-fraction, two types of systematic lumped-parameter models are developed in this study for efficiently representing the dynamic behavior of unbounded soil. Concise formulation is first employed to represent the foundation compliance with a ratio of two polynomials. By defining a quadratic error function, the optimal coefficients of the polynomials can be directly solved from a system of linear equations. Through performing partial-fraction expansion on this polynomial-fraction and designing two basic discrete-element models corresponding to the partial fractions, systematic lumped-parameter models can be conveniently established by connecting these basic units in series. This way of physical realization leads to the first “in-series” type of lumped-parameter model. On the other hand, the reciprocal of the determined polynomial-fraction is taken to stand for the foundation impedance and then decomposed into a linear polynomial and another polynomial-fraction. The “nested division” is subsequently operated to generate a nested form for this polynomial-fraction, which directly corresponds to a nested discrete-element model. Another physical realization referred to as the “nested” type of lumped-parameter model is then easily constructed based on this nested discrete-element model. Since both types of systematic lumped-parameter models are configured without introducing any mass, the foundation input motion can be directly applied to these two models for their applications to the analysis of seismic excitation.The accuracy of these two types of models is first examined in representing the impedance functions for various foundation systems. Comparison of both models with the other existing lumped-parameter models is also made to illustrate their advantages in requiring fewer parameters and featuring a more systematic expansion. A numerical example integrating the lumped-parameter models with the structural parameters to perform simplified SSI analysis for seismic excitations is finally presented.
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