The dynamic response of infinitely long constrained bars and its application for modelling SSI

In dynamic analysis of complex systems usually simplified models are used. In case of floor vibration, an SDOF model is used to calculate the acceleration of the structure, in the seismic design of structures lumped parameter models are recommended to include the effect of the soil-structure interaction (SSI) in the analysis. Nonetheless, for rib stiffened floors, and for finite depth soil layers under the structure these models can be very inaccurate. In these cases (infinitely) long constrained bars (or beams) are recommended as simplified models. In this article an infinitely long, axially constrained bar connected parallelly to a mass-spring system is analysed. An analytical solution is derived, and the impedance functions are determined, which are significantly different from those of simple lumped parameter models. It is shown that this simple model, which depends only on three parameters, is an excellent tool for determining the response of structures excited by horizontal harmonic or earthquake loads, where SSI plays an important role.