On an elastic dissipation model as continuous approximation for discrete media

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

Mathematical Problems in Engineering, 2006, vol. 2006, 1-8

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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:027373

DOI: 10.1155/MPE/2006/27373

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