ON THE DYNAMIC VIBRATIONS OF AN ELASTIC BEAM IN FRICTIONAL CONTACT WITH A RIGID OBSTACLE

Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior o f an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. Ho wever, the horizontal motion of the free end is restricted by the pres ence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different way s. The first involves the classic Signorini unilateral or nonpenetrati on conditions and Coulomb's law of dry friction; the second uses a nor mal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of d amping, existence of a solution is established for a problem in which the normal contact stress is regularized.