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Dynamic stiffness of unbounded medium based on damping‐solvent extraction
Author(s) -
Song Chongmin,
Wolf John P.
Publication year - 1994
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.4290230205
Subject(s) - stiffness , damping matrix , stiffness matrix , matrix (chemical analysis) , direct stiffness method , finite element method , mathematical analysis , taylor series , bounded function , anisotropy , structural engineering , materials science , mathematics , physics , engineering , composite material , quantum mechanics
In the damping‐solvent extraction method, to calculate the dynamic‐stiffness matrix of an unbounded medium, a finite region of the medium, adjacent to the structure is analysed in the first step, whereby hysteretic material damping is introduced artificially as a solvent. This leads to the dynamic‐stiffness matrix of the damped bounded medium, which is assumed in the second step to be equal to that of the damped unbounded medium. In the third step, the effect of the material damping on the dynamic‐stiffness matrix is eliminated, i.e. the damping solvent is extracted, resulting in the dynamic‐stiffness matrix of the unbounded medium. The damping‐solvent extraction method permits an efficient calculation of the dynamic‐stiffness matrix of an unbounded medium by analysing the adjacent bounded medium only, which exhibits the same dynamic characteristics as the (bounded) structure. The familiar standard finite‐element method is sufficient for the analysis and the hysteretic damping is introduced by multiplying the elastic moduli by 1 + 2i£. The introduced hysteretic material damping, the solvent, is extracted at the end of the analysis for each coefficient of the dynamic‐stiffness matrix and for each frequency independently of the others by a very concise equation based on a Taylor expansion. The method is evaluated thoroughly for dynamic soil‐structure interaction and for seismic reservoir‐dam interaction using stringent simple cases with analytical solutions available and is also applied to practical examples, by calculating the dynamic‐stiffness matrix of a semi‐infinite wedge and an embedded foundation.