Y. Dumont, K. L. Kuttler and M. Shillor

A model for the vibrations of a beam with a slider is derived, analysed and
numerically simulated. It describes a viscoelastic beam that is clamped at one
end to a vibrating device while the other end moves between two stops attached
to a slider. The contact is describd by the normal compliance condition which
represents flexible stops. The existence of a weak solution is shown using the
theory of set-valued pseudomonotone operators. The uniqueness of the
weak soluiton is established when the beam is viscoelastic. The model is
discretized using a fourth order spatial discretization and numarically simulated
and the results presented. The dynamics of the vibrations are depicted and so
are the noise characteristics of the system.