Novel Nonlinear Dynamic Beam–Foundation Interaction Model

Abstract

A nonlinear dynamic framework for the analysis of beam–foundation interaction is developed. The extended Hamilton’s principle is used to analyze the response of Euler–Bernoulli beams vibrating on nonlinear continuums (e.g., soils) and subjected to vibrating and moving loads. The continuum beneath the beam is characterized by a nonlinear elastic constitutive relationship that connects the secant shear modulus to the induced strain. The novel feature of the analysis is that the nonlinear compression and shear parameters ks and ts of the continuum (i.e., foundation) do not have to be assumed a priori, as is required in conventional beams on foundation analysis, and are obtained as part of the solution. In fact, it is shown that these parameters are not constant but change with time and depend on the beam–foundation interaction. Another novel feature of the analysis is that the mass of the foundation participating in the vibration is obtained as part of the solution and does not have to be assumed a priori. Thus, the analysis rigorously takes into account the nonlinear beam–foundation (soil–structure) interaction within a dynamic time-integration framework. The developed framework is as accurate as and about 50% faster than conventional nonlinear dynamic finite element analysis. Inputs to the analysis can be given in the form of a text file without any requirement of numerical mesh generation, making the approach rather user friendly. The characteristics of the developed nonlinear dynamic foundation model are illustrated through examples of moving and vibrating loads.