Dynamics of Elastic Objects under Movable Inertial Loading - Some Features of the Mathematical Models and Analogies

Abstract:

This paper describes some features and analogies of the mathematical models for the elastic elements with movable load and for the elastic elements of changeable length. In these systems two forms of own oscillations - the own component and the accompanying one, displaced in phase to the right angle correspond to every frequency of the system. The accompanying component is caused by the mobile inertia load or by the changeable length and they are not trivial only when this factor exists. As for objects with time-varying length, these problems lie in outside of the scope classical problems of mathematical physics due to that the eigenfrequencies and eigenforms become time-dependent functions. This non-classical section of the mathematical physics is waiting for its development, new researches and generalizations.

• Periodical: Materials Science Forum (Volume 968)
• Pages: 427-436
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.968.427
• Online since: August 2019
• Authors: Anatoliy G. Demianenko*
• Keywords: Critical Speed, Dynamics, Frequency, Inertia Load, Varying Length

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DOI: 10.1007/bf02084154