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...

Based on a distributed parameter model for vibrations, an approximate nite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with Kelvin-Voigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several...

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...

The aim of this work is to study a class of nonsmooth dynamic contact problem which model several surface interactions, including relaxed unilateral contact conditions, adhesion and Coulomb friction laws, between two viscoelastic bodies of Kelvin-Voigt type. An abstract formulation which generalizes these problems is considered and the existence of a solution is proved by using Ky Fan’s fixed p...

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...

Zusammenfassung Dieser Beitrag behandelt die Approximation linearer verteilt-parametrischer Systeme zweiter Ordnung mittels eines Galerkin-Ansatzes. Das resultierende endlich-dimensionale Approximationsmodell besitzt ebenfalls die Struktur zweiter Ordnung und ist wie das Originalsystem asymptotisch stabil und passiv. Es wird gezeigt, wie die Freiheitsgrade der Galerkin-Approximation zu wählen s...

In this manuscript, exact solutions of the Oskolkov equation, which describes dynamics incompressible viscoelastic Kelvin-Voigt fluid, are presented. The -expansion method is used to search for these solutions. obtained analyzed with help appropriate parameters and presented graphics. applied efficient reliable fundamental nonlinear waves that enrich various dynamical models seen in engineering...