Mathematical Simulation of Oscillations of a String with Movable Bearing in a Vertical Plane

Authors

  • Viktor Legeza
  • Ivan Dychka
  • Dmytro Legeza

DOI:

https://doi.org/10.20535/1810-0546.2013.1.90706

Abstract

We consider the natural oscillations of the string whose left end is fixed and the right one has the ability to move in a vertical plane by a defined law. We should address this issue to construct an adequate mathematical model of the electric wire taking into account longitudinal displacement of one of its ends. The right-hand mobile support is a commuting pendant with electric wire in the form of insulator strings. The purpose of research is to show and justify the boundary conditions occurring during vibration of a string considering the movements of its right pillar and solve the corresponding boundary problem. The technique for solving the boundary value problem lies in the state that the solution of the wave equation should be searched in such a form that its time-average standard deviation derived from the boundary condition should be minimal. Emphasized should be the obtained research results: change of fundamental frequency of basic tone of string vibrations caused by its right pillar movement in vertical plane within the range of parameters change of the considered system can be neglected.

References

1. Савин Г.Н., Горошко О.А. Динамика нити переменной длины: применительно к шахтным подъемам. — К.: Изд-во АН УССР, 1962. — 331 с.

2. Графский И.Ю., Казакевич М.И. Аэродинамика плохо- обтекаемых тел. — Днепропетровск: ДГУ, 1983. — 116 с.

3. Казакевич М.І. Проблеми стабілізації вант // Металеві конструкції. — 2011. — 17, № 2. — С. 63—64.

4. A. Preumont and Y. Achkire, “Active damping of structures with guy cables”, AIAA, J. of Guidance, Control, and Dynamics, vol. 20, no. 2, pp. 320—326, 1997.

5. Y. Achkire et al., “Active damping and flutter control of cable stayed bridges”, J. of Wind Eng. and Industrial Aerodynamics, vol. 74—76, pp. 913—921, 1998.

6. A. Preumont et al., “Active tendon control of large trusses”, AIAA J., vol. 38, no. 3, pp. 493—498, 2000.

7. Ден-Гартог Дж.П. Механические колебания. — М.: Физматгиз, 1960. — 464 с.

8. Бекметьев Р.М., Жакаев А.Ш., Ширинских Н.В. Пляска проводов воздушных линий электропередач. — Алма-Ата: Изд-во “Наука” Казахской ССР, 1979. — 152 с.

9. Крижов Г.П., Удод Т.Є., Гримуд Г.І. Ожеледно-вітрові навантаження, галопування проводів повітряних ліній електропередавання та боротьба з ними: Довідко- во-метод. посібник. — К.: Мінпаливенерго України, 2010. — 454 с.

10. Нарожний В.Б., Княжевська С.Я., Глей Л.В. Кліматичні навантаження на повітряні лінії електромереж. — К.: Енергопрогрес, 1994. — 212 с.

11. Мартиненко М.А., Легеза В.П., Іванова Ю.І. Математична фізика: Підручник для студентів ВНЗ. — К.: Четверта хвиля, 2009. — 480 с.

Downloads

Published

2013-02-28

Issue

No. 1 (2013): Engineering

Section

Art

License

Copyright (c) 2013 NTUU KPI Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under CC BY 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work