Substatiation of boundary conditions when during interaction of a string with bending hardness with roller basis


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Abstract

The paper considers the problem of vibrations in flexible link with bending hardness when one of the basis is a roller or a pulley. When vibrating the touch point link moves along the basis. Movement of touch point depends on the vibrating process that makes the problem non-linear. Using decomposition function describing vibrations in the number of touch points, boundary conditions are received when link and basis are interesting. Rating of dependence of frequency vibrations on amplitude is received. Stated, that at low amplitude vibrations boundary conditions can be written in the form of equality of angle to zero and displace of flexible link. Error when using such boundary conditions increases with increasing amplitude.

About the authors

Valeriy N Anisimov

Syzran Branch of Samara State Technical University

Email: anisimovl70159@mail.ru
(к.ф.-м.н., доцент), доцент, каф. общетеоретических дисциплин; Сызранский филиал Самарского государственного технического университета; Syzran Branch of Samara State Technical University

Vladislav L Litvinov,

Syzran Branch of Samara State Technical University

Email: vladlitvinov@rambler.ru
преподаватель, каф. общетеоретических дисциплин; Сызранский филиал Самарского государственного технического университета; Syzran Branch of Samara State Technical University

Alexey E Lukyanov

Syzran Branch of Samara State Technical University

(к.ф.-м.н.), доцент, каф. общетеоретических дисциплин; Сызранский филиал Самарского государственного технического университета; Syzran Branch of Samara State Technical University

References

  1. Самарин Ю. П. Об одной нелинейной задаче для волнового уравнения в одномерном пространстве// ПММ, 1964. - Т. 26, №3. - С. 77-80.

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