Deflection and Stresses in Beams joined together by a Continuous Spring Layer

In this report, we develop analytical models and implement numerical schemes to represent a coupled mechanical system of deflections and stresses in beams joined together by a continuous spring layer. We begin by considering a one-dimensional and uniform rectangular beam resting on a continuous layer of elastic material coupled with another rectangular beam beneath the elastic material. Following the formulation and nondimensionalization of the governing system, we consider an analysis of steady states, an inverse design problem, and the dynamics of the linearized model. Numerical simulations of the dynamics are carried out for the one- and two-dimensional models. An asymptotic analysis for nonlinearly coupled beams is also considered.