Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Victor A. Kovtunenko

(1) Dept. of Mathematics and Scientific Computing, Karl-Franzens University, NAWI Graz, Graz, Austria
(2) Lavrent'ev Institute of Hydrodynamics, Siberian Division of the Russian Academy of Sciences, Novosibirsk, Russia

victor.kovtunenko@uni-graz.at

Keywords

  • Dynamic Euler-Bernoulli beam
  • rail road
  • granular foundation
  • semi-linear hyperbolic equation
  • energy inequality

Mathematics Subject Classification

35L76, 37K58, 74E20

Suggested citation

V. A. Kovtunenko. “A Snowpiercer Model: Dynamic Beam Solution for Highly Nonlinear Reaction, Energy Inequality, and Granular Foundation.” Journal of Convex Analysis 34 (2027), No. 1, 408–414. https://doi.org/10.68381/jca34027

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