A dynamic Euler–Bernoulli beam equation frictionally damped on an elastic foundation. (April 2022) - Heibig, Arnaud; Petrov, Adrien
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.