On an elastic dissipation model as continuous approximation for discrete media

Andrianov, I. V.; Awrejcewicz, J.; Ivankov, A. O.

doi:https://doi.org/10.1155/MPE/2006/27373

Mathematical Problems in Engineering

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Volume 2006 | Article ID 027373 | https://doi.org/10.1155/MPE/2006/27373

On an elastic dissipation model as continuous approximation for discrete media

I. V. Andrianov,¹J. Awrejcewicz,²and A. O. Ivankov³

Received18 Aug 2006

Accepted13 Sept 2006

Published30 Oct 2006

Abstract

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.

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Copyright

Copyright © 2006 I. V. Andrianov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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