Size-dependent dynamic response of microstructured elastic substrate under moving loads

Abstract

This study examines the dynamical response of a plane strain isotropic elastic gradient half-plane and a layer resting on a rigid foundation when subjected to a steady-state moving surface load. In the framework of the Mindlin’s Form III gradient theory, the displacement general solutions and associated stress fields are derived through Fourier transforms and Galilean transformation. The formulation incorporates also micro-inertia effects. The investigation is confined to load velocities within the sub-Rayleigh regime. Simulations of the moving load problem in gradient elasticity show significant deviations from lower-grade theories. For layered materials, four possible substrate interface conditions are considered which significantly impact the stress distributions throughout the medium. The maximum normal traction approaches infinity near the Rayleigh speed limit, though a slight decrease is sometimes observed just before reaching this velocity.