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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.
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Victor A. Kovtunenko (2026) studied this question.
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