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Foundation Vibration Analysis Using Simple Physical Models by John P. Wolf

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Appendix B. Consistent Lumped-Parameter Model

A lumped-parameter model to represent the unbounded (linear) soil in a soil-structure-interaction analysis consists of one or several springs, dashpots, and masses with frequency-independent real coefficients. In such a discrete physical model besides the foundation node additional nodes with degrees of freedom can be introduced. The finite-element discretization of the bounded structure and the lumped-parameter model of the unbounded soil will both lead to stiffness, damping, and mass matrices of finite dimensions, which can be assembled straightforwardly to describe the behavior of the total dynamic system.

The discrete-element representations of the translational and rotational cones are the building ...

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