Study on Elastic Rod Oscillations Considering Material Relaxation Properties View Full Text


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Chapter Info

DATE

2021-04-01

AUTHORS

A. V. Eremin

ABSTRACT

A mathematical model for elastic oscillations of a longitudinal rod has been developed on the basis of relaxation terms in the Newton’s second law. An exact analytical solution of the corresponding boundary value problem has been obtained using the method of separation of variables. The analysis of the obtained solution showed that taking into account the medium relaxation properties has a significant effect on the oscillatory process: the amplitude of the oscillations and the shape of the wave profile. Taking into account relaxation coefficients leads to the smoothing of the wave, eliminating jumps in the unknown displacement function. The author estimated for the first time, the influence of high-order derivatives in a modified equation of motion on an oscillatory process. It is shown that high-order derivatives, at a sufficiently large value of the relaxation coefficients, reduce the intensity of the oscillatory process. In this case, the delay of the displacement function in time occurs (compared to the case when the relaxation properties are not taken into account). The theoretical and experimental studies performed made it possible to determine the values of the relaxation and resistance coefficients. More... »

PAGES

1079-1085

Book

TITLE

Proceedings of the 6th International Conference on Industrial Engineering (ICIE 2020)

ISBN

978-3-030-54813-1
978-3-030-54814-8

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-030-54814-8_124

DOI

http://dx.doi.org/10.1007/978-3-030-54814-8_124

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1136818513


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