Systematic lumped‐parameter models for foundations based on polynomial‐fraction approximation

Abstract

SUMMARYBased on the approximation by polynomial-fraction, a series of systematic lumped-parameter models are developed in this paper for e ciently representing the dynamic behaviour of unbounded soil. Concise formulation is ÿrst employed to represent the dynamic exibility function of foundation with a ratio of two polynomials. By deÿning an appropriate quadratic error function, the optimal coe cients 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. Since the systematic lumped-parameter models are conÿgured without introducing any mass, the foundation input motion can be directly applied to these models for their applications to the analysis of seismic excitation. The e ectiveness of these new models is strictly validated by successfully simulating a semi-inÿnite bar on an elastic foundation. Subsequently, these models are applied for representing the dynamic sti ness functions for di erent types of foundation. Comparison of the new 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.

Efficient Modelling of Wind Turbine Foundations

“…Hence, the need arises for a computationally efficient model which accounts for the interaction of a wind turbine foundation with the surrounding/underlying soil. A fairly general solution is the so-called lumped-parameter model, the development of which has been reported by Wolf (1991a), Wolf & Paronesso (1991), Wolf (1991b), Wolf & Paronesso (1992), Wolf (1994), Wolf (1997), Wu & Lee (2002), and Wu & Lee (2004). The present section is, to a great extent, based on this work.…”

Probabilistic impedance of foundation: Impact of the seismic design on uncertain soils

“…Some examples of these models can be found in [22][23][24][25][26][27][28]. They provide simple descriptions of the soil as equivalent models of springs, dashpots, and masses, the values of which are identified from an impedance computed with an alternative method (e.g.…”

Nested lumped‐parameter models for foundation vibrations

“…Based on the work by Wu and Lee [4] to determine a doubly asymptotic polynomial-fraction for approximating the dynamic exibility function of foundation, other nested types of systematic lumped-parameter models for unbounded soil are further developed in the present article.…”

“…Each of these fractions was then associated with a certain type of fundamental discrete model and connected in parallel to build the lumped-parameter model. More recently, e cient formulation was employed by Wu and Lee [4] to represent the dynamic exibility function of foundation with a ratio of two polynomials. Through performing partial-fraction expansion on this polynomial-fraction and designing two basic discrete-element models corresponding to the partial fractions, systematic lumpedparameter models can be conveniently established by connecting these basic units in series.…”