Premium
Consistent lumped‐parameter models for unbounded soil: Physical representation
Author(s) -
Wolf John P.
Publication year - 1991
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290200103
Subject(s) - damper , representation (politics) , frequency domain , time domain , differential equation , mathematics , stiffness , mathematical analysis , control theory (sociology) , computer science , structural engineering , engineering , control (management) , artificial intelligence , politics , political science , law , computer vision
A systematic procedure to develop a consistent lumped‐parameter model with real frequency‐independent coefficients to represent the unbounded soil is developed. Each (modelled) dynamic‐stiffness coefficient in the frequency domain is approximated as a ratio of two polynomials, which is then formulated as a partial‐fraction expansion. Each of these terms is represented by a discrete model, which is the building block of the lumped‐parameter model. A second‐order term, for example, leads to a discrete model with springs and dampers with two internal degrees of freedom, corresponding to two first‐order differential equations, or, alternatively, results in a discrete model with springs, dampers and a mass with one internal degree of freedom, corresponding to one second‐order differential equation. The lumped‐parameter model can easily be incorporated in a general‐purpose structural dynamics program working in the time domain, whereby the structure can even be non‐linear. A thorough evaluation shows that highly accurate results are achieved, even for dynamic systems with a cutoff frequency.