%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/