On boundary feedback stabilisability of a viscoelastic beam

Abstract

SynopsisIt is shown that a cantilevered beam with weak viscoelastic damping of Boltzmann-type can be uniformly stabilised by velocity feedback applied as a shearing force at the free end of the beam. Estimates for the viscoelastic energy are derived using the energy multiplier method. The energy decay is related to the decay of the relaxation modulus associated with the viscoelastic material.