Matrix Formulation of Foundations for Vibrating Machinery in Frequency Domain

Abstract

A matrix formulation to study the coupled response of rigid foundations modelled by springs and dashpots is presented. Springs and dashpots orientation can be any possible, thus a general solution is determined. Response in terms of displacements and rotations is determined from a matrix system in the complex field. The physics of the problem presented here has been extensively studied and a broad range of useful formulas to determine springs and dashpots properties in soil-structure interaction is available, however it has also been identified that there are some limitations on coupling various degrees of freedom in the available formulations. Then, the novelty of the approach presented comes from the matrix manipulation that leads to an expression that provides a closer approximation to the real phenomenon, because all degrees of freedom can be coupled. This approach may allow to the analyst finding a coupled response including the cases when either springs or dashpots are not orthogonally oriented. In an example at the end of this study, the influence of one of the involved parameters in the soil-structure analysis is pointed out.