#2353. A dynamic Euler–Bernoulli beam equation frictionally damped on an elastic foundation

August 2026publication date
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Journal’s subject area:
Economics, Econometrics and Finance (all);
Analysis;
Applied Mathematics;
Computational Mathematics;
Engineering (all);
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Abstract:
This paper deals with a dynamic Euler–Bernoulli beam equation. The beam relies on a foundation composed of a continuous distribution of linear elastic springs. In addition to this time dependent uniformly distributed force, the model includes a continuous distribution of Coulomb frictional dampers, formalized by a partial differential inclusion. Under appropriate regularity assumptions on the initial data, the existence of a weak solution is obtained as a limit of a sequence of solutions associated with some physically relevant regularized problems.
Keywords:
Coulomb friction law; Euler–Bernoulli beam equation; Existence result

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