A dynamic Euler–Bernoulli beam equation frictionally damped on an elastic foundation. (April 2022)

• Record Type: Journal Article
• Authors: Heibig, Arnaud; Petrov, Adrien
• Is Part Of: Nonlinear analysis. Volume 64(2022)
• Publication Date: 2022-04
• Subjects: Euler–Bernoulli beam equation -- Coulomb friction law -- Existence result; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103427
• Languages: English
• ISSNs: 1468-1218

Abstract

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.