The eigenmode expansion method for oscillations of an elastic body with internal and external friction

A method is proposed for solving dynamical problems for a viscoelastic body (the Kelvin-Voigt model) in a massless viscous medium. Interaction with the external medium produces on the boundary of the body stresses proportional to the rate of displacement. The model of external friction is that used for modelling dynamical processes in elastic media filling an infinite domain 1, 2]. The implementation of numerical methods of solution requires an equivalent restatement of the problem in a finite domain, using external viscous friction to allow for the radiation of energy at infinity.