Existence for dynamic contact of a stochastic viscoelastic Gao Beam

This work presents and analyzes a model for the vibrations of a viscoelastic Gao Beam, which may come in contact with a deformable random foundation and allows for stochastic inputs. The body force involves a stochastic integral that includes Brownian motion. In addition, the gap between the beam and the foundation is a stochastic process, which is one of the novelties in the paper, and contact is described with the normal compliance condition. The existence and uniqueness of strong solutions to the model is established and it is shown that the solutions are adapted to the filtration determined by a given Wiener process for the stochastic force noise term.