Coupling Modal Analysis with the BEM for the Transient Response of Bar Structures Interacting with Three-Dimensional Soil Profiles

This work investigates the transient response of bar structures interacting with three-dimensional soil profiles. The structures are modeled by the Finite Element Method (FEM) and the soil models are described by a three-dimensional Boundary Element Formulation (BEM) in the frequency domain. A classic modal analysis is performed on the structure in terms of the relative displacements with respect to the soil. The dynamic response of the structure is coupled to the soil response, aiming to obtain frequency response functions (FRFs) of the soil-structure system. A new set of modal parameters are extracted from the FRFs of the coupled system. These new parameters allow for the synthesis of a set of orthogonal differential equations in the time domain. These equations are integrated by a classical numerical scheme resulting in the transient response of the structure interacting with the supporting soil. It is shown that for soil profiles that present eigenfrequencies, the system modal basis must be expanded to properly include the soil dynamics. The cases of a structure interacting with a homogeneous half-space and with a horizontal layer over a rigid stratum are considered. The results presented for both soil models are consistent.