In this paper it is shown that the change in the energy for a linearly viscoelastic body (with Kelvin–Voigt type viscosity) in frictionless contact with a rigid obstacle can be accounted for by viscous losses and the work done by external forces. Thus there is no change in the energy due to impacts, unlike the case of rigid-body dynamics. The result can be extended to a wide class of dynamic vi...

We study output tracking and disturbance rejection for an Euler-Bernoulli beam with Kelvin-Voigt damping. The system has distributed control pointwise observation. As our main result we design a finite-dimensional low-order internal model based controller that is on spectral Galerkin method reduction by Balanced Truncation. performance of the designed demonstrated numerical simulations compared...

We extend the study [1] devoted to the dynamic response of a structure made of two linearly elastic bodies connected by a thin soft adhesive layer made of a Kelvin Voigt type nonlinear viscoelastic material to the case of a Generalized Standard Material with a positive definite quadratic density of free energy. A concise formulation in terms of an evolution equation in a Hilbert space of possib...