DYNAMICS OF A RIGID BEAM ON AN ELASTIC SINGLE-LAYER FOUNDATION WITH MECHANICAL CHARACTERISTICS VARYING WITH DEPTH

Abstract

The dynamic response of rigid structures resting on elastic foundations is a fundamental problem in civil and seismic engineering, especially when accounting for spatial variability in soil properties. Traditional models such as Winkler’s foundation fail to capture the continuous distribution of soil deformation and reactive forces accurately. This study addresses this gap by formulating and solving the problem of a rigid beam resting on an elastic single-layer foundation with depth-dependent mechanical characteristics. Using the variational principle of V.Z. Vlasov, the authors derive integro-differential equations governing beam oscillations under seismic loading, incorporating wave propagation velocity and variable soil density. Numerical simulations and frequency response analyses reveal that the amplitude of oscillation is finite even at resonant frequencies—unlike in simpler models—and strongly depends on soil layer thickness and stiffness. These findings have important implications for the realistic modeling of soil-structure interaction, contributing to safer and more efficient structural design in earthquake-prone regions.