Matrix Formulation of Foundations for Vibrating Machinery in Frequency Domain

Abstract

A matrix formu la tion to study the coupled response of rigid foun da tions modelled by springs and dashpots is presented. Springs and dashpots orien ta tion can be any possible, thus a general solu tion is deter mined. Response in terms of displacements and rota tions is deter mined from a matrix system in the complex field. The physics of the problem presented here has been exten sively studied and a broad range of useful formulas to deter mine springs and dashpots prop er ties in soil-struc ture inter ac tion is avail able, however it has also been iden ti fied that there are some limi ta tions on coupling various degrees of freedom in the avail able formu la tions. Then, the novelty of the approach presented comes from the matrix manip u la tion that leads to an expres sion that provides a closer approx i ma tion to the real phenom enon, 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 orthogo nally oriented. In an example at the end of this study, the influ ence of one of the involved param e ters in the soil-struc ture anal ysis is point ed out.