%0 Journal Article
%T On an elastic dissipation model as continuous approximation for discrete media
%A I. V. Andrianov
%A J. Awrejcewicz
%A A. O. Ivankov
%J Mathematical Problems in Engineering
%D 2006
%I Hindawi Publishing Corporation
%R 10.1155/mpe/2006/27373
%X Construction of an accurate continuous model for discrete media is an important topic in various fields of science. We deal with a 1D differential-difference equation governing the behavior of an n-mass oscillator with linear relaxation. It is known that a string-type approximation is justified for low part of frequency spectra of a continuous model, but for free and forced vibrations a solution of discrete and continuous models can be quite different. A difference operator makes analysis difficult due to its nonlocal form. Approximate equations can be obtained by replacing the difference operators via a local derivative operator. Although application of a model with derivative of more than second order improves the continuous model, a higher order of approximated differential equation seriously complicates a solution of continuous problem. It is known that accuracy of the approximation can dramatically increase using Padé approximations. In this paper, one- and two-point Padé approximations suitable for justify choice of structural damping models are used.
%U http://www.hindawi.com/journals/mpe/2006/027373/abs/