| Issue |
MATEC Web Conf.
Volume 224, 2018
International Conference on Modern Trends in Manufacturing Technologies and Equipment (ICMTMTE 2018)
|
|
|---|---|---|
| Article Number | 02044 | |
| Number of page(s) | 6 | |
| Section | General problems of mechanical engineering: design, optimization, maintenance | |
| DOI | https://doi.org/10.1051/matecconf/201822402044 | |
| Published online | 30 October 2018 | |
Nonlinear waves in an elastic guide interacting with an elastic-inertial foundation
Mechanical Engineering Research Institute of RAS, Nizhny Novgorod, Russia
* Corresponding author: aleonav@mail.ru
This paper deals with the study of the transverse wave propagation in a string resting on an elastic-inertial foundation. A self-consistent dynamic problem is herein considered for a system composed of a one-dimensional flexible guide (string) and an elastic-inertial foundation. As a foundation model the Vesnitsky’s model was chosen. The set of equations is reduced to one fourth-order cubic-nonlinear equation relative to transverse displacements of the string. Depending on the string and the elastic-inertial foundation mass ratio, the evolutionary equation has the following three extreme events: the modified Ostrovsky equation, the Riemann equation with a cubic nonlinearity, the equation for an anharmonic oscillator with a cubic nonlinearity.
© The Authors, published by EDP Sciences, 2018
This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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