A dynamic Euler-Bernoulli beam equation frictionally damped on an elastic foundation (Q2061597)

The steady-state solution of an Euler-Bernoulli beam subjected to the action of a time-dependent uniformly distributed force on a foundation composed of a continuous distribution of linear elastic springs associated in parallel with an approximate/abstract distribution of Coulomb frictional dampers is studied in this paper, which starts with a general abstract existence result in the spirit of Hille-Yosida theorem. The existence of a weak solution is also achieved as a limit of a sequence of solutions for some physically relevant regularised problems under proper regularity assumptions on the original data.