Numerical Study of Forced Vibration Suppression by Parametric Anti-Resonance

Open access

Abstract

The parametric anti-resonance phenomenon as an active damping tool for suppression of externally excited resonant vibration is numerically studied herein. It is well known fact that the anti-resonance phenomenon, i.e. the stiffness periodic variation by subtractive, combination resonance frequency, brings stabilization and cancelling into self-excited vibrations. But this paper aims at a new possibility of its application, namely a damping of externally excited resonant vibration. For estimation of its effect we come both from a characteristic exponent of the analytical solution and numerical solution of forced vibration of 2DOF linear system with additional parametric excitation. The amplitude suppression owing to the parametric anti-resonance is studied on several parameters of the system: a depth of parametric excitation, mass ratio, damping coefficient and small frequency deviations from the parametric anti-resonance.

1. Ecker H., Pumhoessel T., Tondl A. (2002), A study on parametric excitation for suppressing self excited rotor vibrations, Proceedings of the 6th Int. Conference on Rotor Dynamics (IFTo MM), Sydney.

2. Ecker H., Tondl A. (2004), Stabilization of a rigid rotor by a time-varying stiffness of the bearing mounts, Proceedings of the 8th Int. Conference on Vibrations in Rotating Machinery, Swansea, Professional Engineering Publishing Limited for the Institution of Mechanical Engineers, Berry St. Edmunds and London, pp. 45-54.

3. Ecker H., Tondl A. (2005), Increasing the stability threshold of a rotor by open-loop control of the bearing mount stiffness, Proceedings of Int. Symposium on Stability Control of Rotating Machinery, Ohio, pp. 351361.

4. Ecker H., Tondl A. (2007), Suppression of selfexcited vibrations in valve systems, Proceedings of Colloquium Dynamics of Machines 2007, Institute of Thermomechanics AS CR, Prague, pp. 55-62.

5. Ecker H. (2010), Exploring the Use of Parametric Excitation, Proceedings of the 10th Int. Conference on Recent Advances in Structural Dynamics, The Institute of Sound and Vibration, UK.

6. Ecker H., Tondl A. (2011), On the Suppression of Flow -Generated Self-Excited Vibrations of a Valve, International Conference on Vibration Problems (ICOVP), Springer Proceedings in Physics 139, Springer, pp. 793-799.

7. Ecker H., Pumhoessel T. (2012), Vibration suppression and energy transfer by parametric excitation in drive systems, Journal of Mechanical Engineering Science, 226, 8, 2000-2014.

8. Dohnal F., Tondl A. (2009), Suppressing Flutter Vibrations by Parametric Inertia Excitation, Journal of Applied Mechanics, 76, 7.

9. Halanay A. (1966), Differential equations - stability, oscillations, time lags, New York, Academy press.

10. Łuczko J., Czerwiński A. (2015), Parametric vibrations of flexible hoses excited by a pulsating fluid flow, Part I: Modelling, solution method and simulation, Journal of Fluids and Structures, 55, 155-173.

11. Nabergoj R., Tondl A., Ecker H. (2006), To the problem of self-excited systems having several unstable vibration modes, Proceedings of the Colloquium Dynamics of Machines 2006, Institute of Thermomechanics AS CR, Prague, pp. 71-78.

12. Nabergoj R., Tondl A., Ecker H. (2007), Additional contribution to the problem of self-excited systems having several unstable vibration modes, Engineering Mechanics, 14, 1/2, 1-12.

13. Mettler E. (1965), Schwingungs- und stabilitatsprobleme bei mechanischen systemen mit harmonischer erregung, ZAMM - Zeitschrift fur Angewandte Mathematik und Mechanik, 45, 7-8, 475-484.

14. Pešek E., Tondl A. (2012), Contribution to application of parametric ‘anti-resonance’ for autoparametric systems, Engineering Mechanics, 19, 5, 1-9.

15. Pešek E., Pust E., Bula Y., Cibulka J. (2015), Application of piezofilms for excitation and active damping of blade flexural vibration, Archives of Acoustics, 40, 1, 59-69.

16. Pumhoessel T., Ecker H., Tondl A. (2011), Zum Einfluss einer periodischen axialen Kraft auf die la teralen Schwingungen eines Laval-Rotors, 9 Tagung Schwingungen in rotierenden Maschinen (SIRM), Darmstadt, pp. 21-23.

17. Tondl A. (1959), Metoda k určení intervalů nestability quasi-harmonických kmitů [The method for the determination of instability intervals of quasi-harmonic vibration systems], Aplikace Matematiky, 4, 4, 278-289.

18. Tondl A. (1998a), To the problem of quenching selfexcited vibrations, Acta Technica CSAV, 43, 109-116.

19. Tondl A. (1998b), Vibration quenching of an externally excited system by means of dynamic absorber, Acta Technica CSAV, 43, 301-309.

20. Tondl A., Ecker H. (1999), Cancelling of self-excited vibrations by means of parametric excitation, Proceedings of ASME Design Engineering Technical Conference, Las Vegas 1999, DETC/VIB-8071.

21. Tondl A., Ruijgrok T., Verhulst F., Naber- GOJ R. (2000), Autoparametric Resonance in Mechanical Systems, Cambridge University Press.

22. Tondl A. (2000a), Suppressing self-excited vibration by means of parametric excitation, Proceedings of Colloquium Dynamics of Machines 2000, Institute of Thermomechanics AS CR, Prague, pp. 225-230.

23. Tondl A. (2000b), Self-excited vibration quenching inarotor system by means of parametric excitation, Acta Technica CSAV, 45, 199-211.

24. Tondl A., Ecker H. (2003), On the problem of selfexcited vibration quenching by means of parametric excitation, Archive of Applied Mechanics, 72, 923-932.

25. Tondl A. (2003), Combination resonance and antiresonances in systems parametrically excited by harmonic variation of linear damping coefficients, Acta Technica CSAV, 48, 239-248.

26. Tondl A., Nabergoj R. (2004), The effect of parametric excitation onaself-excited three-mass system, International Journal of Non-linear Mechanics, 39, 821-832.

27. Tondl A. (2008a), Passive and active means for selfexcited vibration suppressing: Two-mass model, Engineering Mechanics, 15, 2, 133-138.

28. Tondl A. (2008b), To the problem of self-excited vibration suppression, Engineering Mechanics, 15, 4, 297308.

29. Tondl A., Pust L. (2010), To the Parametric Anti Resonance Application, Engineering Mechanics, 17, 2, 135-144.

30. Tondl A., Pust L. (2011), Further application of parametric anti-resonance, Proceedings of the Colloquium Dynamics of Machines 2011, Institute of Thermomechanics AS CR, Prague, pp. 97-104.

31. Tondl A., Pust L. (2012), On the phenomenon “Parametric anti-resonance”, Strojnicky Casopis, 63, 3, 125-137.

Archives of Acoustics

The Journal of Institute of Fundamental Technological of Polish Academy of Sciences

Journal Information


IMPACT FACTOR 2016: 0.816
5-year IMPACT FACTOR: 0.835

CiteScore 2016: 1.15

SCImago Journal Rank (SJR) 2016: 0.432
Source Normalized Impact per Paper (SNIP) 2016: 0.948

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 172 146 5
PDF Downloads 67 61 7