Mathematical Modelling of Dynamics of the Vibroprotective System Equipped with Roller Absorber

Authors

  • Дмитро Вікторович Легеза NTUU KPI, Ukraine

DOI:

https://doi.org/10.20535/1810-0546.2014.6.35941

Keywords:

Vibroprotective system, Isochronous roller absorber, Brachystochrone for a roller, Settled forced oscillations, Amplitude-frequency characteristic, Parameters of tuning of absorber

Abstract

Using the methods of mathematical modeling to develop numeral-analytical approach for determination of equations of ACHKH of the nonlinear vibroprotective system with a new isochronous roller absorber in the first approaching and to define the optimum parameters of its tuning. For the conclusion of equations ACHKH the averaging method of W. Ritz, adapted to the probed task, was used. For the solution of nonlinear algebraic equations of ACHKH of the system the special programmatic complex was developed in a non-obvious form. For determination of optimum parameters of tuning of roller absorber, a numeral-graphic method is offered and a numeral experiment is conducted on determination of the indicated parameters. It is set on the basis of numeral experiment, that the own frequency of the optimum adjusted absorber in the nonlinear raising does not coincide with the own frequency of the optimum adjusted absorber in the linear raising. In addition, the maximal values of amplitudes of bearing body for linear and nonlinear tasks differ substantially: a rejection makes about 10 % (less than for a nonlinear task).  Main advantage of the offered roller absorber consists of that frequency of own oscillations of absorber does not depend on the relative rejections of its working body. Therefore even at the large relative rejections of working body of absorber originally adjusted his parameters remain stable, and oscillations – isochronous. It is determined that the offered absorber is effective enough: it is possible using it to decrease substantially the level of amplitudes of the forced oscillations of bearings bodies.

Author Biography

Дмитро Вікторович Легеза, NTUU KPI

Legeza Dmytro V., postgraduate student

References

Кондра М.П., Остроумов Б.В. Опыт применения динамических гасителей колебаний для виброзащиты башен // Докл. на Междунар. симп. “Виброзащита в строительстве”. – Л.: ЦНИИСК им. В.А. Кучеренко, 1984. – 2. – С. 33–34.

Остроумов Б.В. Исследование, разработка и внедрение высотных сооружений с гасителями колебаний: Автореф. докт. техн. наук. – М.: ЗАО “ЦНИИПСК им. Мельникова”, 2003. – 48 с.

Коренев Б.Г., Резников Л.М. Динамические гасители колебаний. – М.: Наука, 1988. – 304 с.

Коренев Б.Г., Маковичка Д., Ройтштейн М.М. Виброзащита башенных конструкций с помощью динамических гасителей колебаний // Staveb. Cas., č. № 9, VEDA, Bratislava. – 1989. – C. 641–651.

Фейгин М.И. К теории ударного демпфера // Изв. ВУЗов. Радиофизика. – 1961. – 4, № 3. – С. 26–33.

Сысоев В.И. Устройства для гашения колебаний: Справочник проектировщика “Динамический расчет зданий и сооружений”. Раздел 16. – М.: Стройиздат, 1984. – С. 264–271.

D.V. Balandin et al., Optimal Protection from Impact, Shock and Vibration. Amsterdam: Gordon and Breach, 2001, 436 p.

O. Fisher, “Same experience with the use of vibration absorbers on aerial masts,” ACTA Technica CSAV, vol. 19, no. 2, pp. 32–38, 1974.

J.C. Snowdon, Vibration and shock in damped mecha­nical systems. N.Y.: John Wiley, 1968, 474 p.

E. Simiu and R.H. Scanlan, Wind effects on structures: Fundamentals and applications to design. 3th ed. N.Y.: John Wiley, 1996, 688 p.

Алексеев А.М., Сборовский А.К. Судовые виброгасители. – Л.: Судпромгиз, 1965. – 192 с.

Шмырев А.Н., Мореншильд В.А., Ильина С.Г. Успокоители качки судов. – Л.: Судпромгиз, 1961. – 516 с.

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

A.S. Richardson, “Method and apparatus for relatively large amplitude type vibrations in electric power trans­mission conductors and other oscillating bodies,” US Patent № 3221093. Int. Cl. H02G 7/14, November 30, 1965.

Патент на корисну модель № 80556. Котковий гаситель для придушення галопування проводів потужних ліній елект­ропередач / В.П. Легеза, Д.В. Легеза, О.В. Бов­кун; Опубл. 10.06.2013 р., Бюл. 11.

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

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.

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

Wang Yuefang and Luo Albert C.J., “Dynamics of traveling inextensible cables,” Commun. Nonlinear Sci. and Nu­mer. Simul., no. 5, pp. 531–542, 2004.

Казакевич М.І. Проблеми стабілізації вант // Металеві конструкції. – 2011. – 17, № 2. – С. 63–84.

Легеза В.П. Віброзахист динамічних систем із котковими гасниками. – К.: Четверта хвиля, 2010. – 280 с.

Патент України на винахід №99759, МПК F16F7/10, E04B1/98. Ізохронний роликовий гасник вимушених коливань / В.П. Легеза, Д.В. Легеза. – Опубл. 25.09.2012; Бюл. № 18.

V.P. Legeza, “Dynamics of vibration isolation system with a quasi-isochronous roller shock absorber,” Int. Appl. Mechanics, vol. 47, no. 3, pp. 329–337, 2011.

V.P. Legeza and D.V. Legeza, “Isochronous Vibrations of a Heavy Cylinder in a Cylindrical Recess”, J. of Auto­mation and Inf. Sci., vol. 44, no. 1, pp. 31–39, 2012.

V.P. Legeza, “Efficiency of a Vibroprotection System with an Isochronous Roller Damper,” Mechanics of Solids, vol. 48, no. 2, pp. 168–177, 2013.

K. Klotter, “Non-linear vibration problem treated by the averaging method of W. Ritz,” Proc. 1-st U.S. Nation. Congr. Appl. Mech., pp. 125–131, 1951.

W. Ritz, “Über eine neue Methode zur Lözung gewisser Variations – Probleme der mathematischen Physik,” J. für die reine und angewandte Mathematik (Crelle), B. 135, no. 1, pp. 1–61, 1909.

W. Weaver et al., Vibration Problems in Engineering, 5th ed. N.Y.: John Wiley, 1990, 624 p.

Published

2015-09-02

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Art