Symmetric matrix-valued transmitting boundary formulation in the time-domain for soil-structure interaction problems

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• 作者：Antonio Cazzani ; Peter Ruge
• 关键词：Symmetric matrix-valued Padé ; interpolation ; Conjugate rational Padé ; function ; Soil&ndash ; rotor&ndash ; foundation interaction ; Dynamic stiffness ; Rotor running through resonance ; Sensitivity of least-square procedure
• 刊名：Soil Dynamics and Earthquake Engineering
• 出版年：February, 2014
• 年：2014
• 卷：57
• 期：Complete
• 页码：104-120
• 全文大小：3660 K

文摘

Time-domain formulations for soil-structure interaction problems with an unbounded soil-domain (the so-called far-field) including wave propagation require such time-domain formulations for both parts, soil and structure. For the structure (the near-field), typically treated by a finite element approach, the time-domain is used from the very beginning of the procedure. However, for the unbounded soil a representation by means of a frequency-dependent dynamic stiffness is usually available and it becomes necessary to devise techniques for switching from the frequency- to the time-domain.

For various special cases in solid mechanics (e.g. plane, cylindrical and spherical waves) one-dimensional formulations in space have been used to derive scalar dynamical stiffness, to establish corresponding rational functions in the frequency-domain and transfer them into the time-domain in order to couple the near- and the far-field.

A complete three-dimensional analysis for pile-groups through a linear homogeneous unbounded soil-domain and the corresponding description in the time-domain have already been treated by Cazzani and Ruge (2012, 2013) by means of a fully matrix-valued rational representation of a set of dynamic stiffness matrices , as a function of the angular frequency . However, the symmetry of the input stiffness has not been maintained for the corresponding representation in the time-domain.

This paper presents a fully matrix-valued rational formulation which does transfer the symmetry of to the corresponding formulation in the time-domain. Thus, the numerical treatment of the whole soil-structure interaction problem, coupling the far-field and near-field systems, can take advantage of algorithms for symmetric algebraic problems.