Strain energy method for solving wave problems of a flexible thread
Authors: Bryukvin A.V., Bryukvina O.Yu.
Published in issue: #5(101)/2020
DOI: 10.18698/2308-6033-2020-5-1977
Category: Mechanics | Chapter: Mechanics of Deformable Solid Body
The paper considers the behavior of a flexible deformable thread when longitudinal and transverse waves pass through it. The processes occurring in a thread during the passage of a wave perturbation through it are analyzed under the assumption that the wave front zone is limited comparing with the length of the thread but not assuming this quantity to be of infinite smallness. In contrast to other similar works, no assumptions were made in advance about the shape of the thread in the zone of the wave perturbation passage (the fracture of the thread) and the dependence of the tension force on its elongation. The only requirement is the implementation of the general theorems of dynamics. Formulas for the relation of the thread speed before and after the passage of the wave with a change in the angle of thread inclination are obtained making possible solving wave propagation problems in a new way. The method is illustrated by new solutions to known problems, which allows comparing the obtained results with known solutions and verifying the advantages of the proposed method.
References
[1] Rakhmatulin H.A., Demyanov Yu.A. Prochnost pri intensivnykh kratkovremennykh nagruzkakh [Strength under intense short-term loads]. Moscow, Logos Publ., 2009, 511 p. ISBN 978-5-98704-422-7
[2] Rakhmatulin Kh.A., Shemyakin E.I., Demyanov Yu.A. Prochnost i razrushenie pri kratkovremennykh nagruzkakh [Strength and fracture under short-term loads]. Moscow, Universitetskaya kniga, Logos Publ., 2008, 624 p.
[3] Demyanov Yu.A. Doklady Akademii nauk — Proceedings of the Academy of Science, 1999, vol. 369, no. 4. pp. 461–465.
[4] Zvyagin A.V., Zubkov A.F., Panfilov D.I. Prikladnaya fizika i matematika —Applied Physics and Mathematics, 2018, no. 3, pp. 50–60.
[5] Demyanov Yu.A., Kokoreva D.V., Malashin A.A. Prikladnaya fizika i matematika — Applied Physics and Mathematics, 2003, vol. 67, no. 2, pp. 272–282.
[6] Zvyagin A.V., Panfilov D.I. Dinamika niti peremennoy dliny [Dynamics of a thread of variable length]. Sbornik nauchnykh statey po itogam mezhdunarodnoy nauchno-prakticheskoy konferentsii [Collection of scientific articles further to results of the international scientific-practical conference]. St. Petersburg, KultInformPress Publ., 2014, pp. 50–56.
[7] Bolotov A.A., Demyanov Yu.A. Prikladnaya matematika i mekhanika — Journal of Applied Mathematics and Mechanics, 2013, vol. 77, no. 1, pp. 161–166.
[8] Demyanov Yu.A., Malashin A.A. Doklady Akademii nauk — Proceedings of the Academy of Science, 2007, vol. 413, pp. 45–49.
[9] Bryukvina O.Yu., Lobachev V.I., Malashin A.A. Vestnik Moskovskogo gosudarstvennogo universiteta lesa / Lesnoy vestnik — Moscow State Forest University Bulletin / Forestry Bulletin, 2012, vol. 6, no. 89, pp. 4–8.
[10] Bryukvin A.V., Bryukvina O.Yu. Vestnik Moskovskogo gosudarstvennogo universiteta lesa / Lesnoy vestnik — Moscow State Forest University Bulletin / Forestry Bulletin, 2008, no. 2, pp. 141–143.
[11] Bryukvin A.V., Bryukvina O.Yu. Lesnoy vestnik — Forestry Bulletin, 2018, vol. 22, no. 2, pp. 134–139. DOI: 10.18698/2542-1468-2018-2-134-139
[12] Bryukvin A.V., Bryukvina O.Yu. Podyemno-transportnoe delo — Lift and Transportation Engineering, 2018, no. 3-4, pp. 6–10.
[13] Malashin A.A., Demyanov Yu.A., Dyakov P.A., Bryukvina O.Yu. Matematicheskoe modelirovanie dinamiki trosovoy sistemy [Mathematical modeling of the cable system dynamics]. Sbornik trudov II Vserossiyskoy nauchno-tekhnicheskoy konferentsii “Mekhanika i matematicheskoe modelirovanie v tekhnike”. Moskva, MGTU im. N.E. Baumana, 22–23 noyabrya 2017 g. [Proceedings of the II All-Russian Scientific and Technical Conference “Mechanics and Mathematical Modeling in Engineering”. Moscow, BMSTU, November 22-23, 2017). Moscow, BMSTU Publ., 2017, pp. 139–144.
[14] Abramyan A.K., Vakulenko S.A., Indeytsev D.A. Izvestiya Rossiyskoy akademii nauk. Mekhanika tverdogo tela — Mechanics of Solids, 2016, no. 5, pp. 94–100.
[15] Malashin A.A., Smirnov N.N., Bryukvina O.Yu., Dyakov P.A. Journal of Sound and Vibration, 2017, vol. 389, pp. 41–51.