A Snowpiercer Model: Dynamic Beam Solution for Highly Nonlinear Reaction, Energy Inequality, and Granular Foundation

The dynamic contact problem for Euler-Bernoulli beam equation with highly nonlinear reaction term is formulated to model deflection of a rail road on a granular foundation under motion of a high-speed vehicle (snowpiercer). Based on the energy inequality and Galerkin approximation, variational solution to the evolutionary semi-linear differential equation is proved. The reaction of the granular foundation is presented for periodic beam vibrations, which illustrate plastic, ageing, and hardening phenomena.