Nested lumped‐parameter models for foundation vibrations

Abstract

SUMMARYThe concept of polynomial-fraction approximation is explored in this article to develop a nested type of systematic lumped-parameter model for unbounded soil. Based on the optimal coe cients determined from the exibility formulation, the reciprocal of the polynomial-fraction is ÿrst taken to represent the dynamic sti ness function of foundation and then decomposed into a linear polynomial and another polynomial-fraction. The nested division introduced in this study is operated to generate a nested form for this decomposed polynomial-fraction, which directly corresponds to a nested discrete-element model. The nested type of lumped-parameter model is then easily constructed by connecting this nested discrete-element model in series with another simple discrete-element model corresponding to the linear polynomial.

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.…”

Simple Models of Foundation-Soil Interactions

“…Then a lumped-parameter model is developed for a foundation-soil system while the foundation Manuscript is massless. Several studies [1]- [11] followed the conventional method addressed above to develop the simplified models. The conventional method used an optimization process to determine the unknown parameters of the lumped-parameter models so that the accuracies of those models were affected by objective functions used in optimization.…”

A discrete model for response estimation of soil-structure systems with embedded foundations

“…The method was later used by other researchers (Wu & Lee, 2002). Following that, another method was developed by using nested divisions, also based on the concept of polynomial fraction (Wu & Lee, 2004).…”