JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Passive suppression of helicopter ground resonance instability by means of a strongly nonlinear absorber
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Passive suppression of helicopter ground resonance instability by means of a strongly nonlinear absorber
Bergeot, Baptiste; Bellizzi, Sergio; Cochelin, Bruno;
 Abstract
In this paper, we study a problem of passive suppression of helicopter Ground Resonance (GR) using a single degree freedom Nonlinear Energy Sink (NES), GR is a dynamic instability involving the coupling of the blades motion in the rotational plane (i.e. the lag motion) and the helicopter fuselage motion. A reduced linear system reproducing GR instability is used. It is obtained using successively Coleman transformation and binormal transformation. The analysis of the steadystate responses of this model is performed when a NES is attached on the helicopter fuselage. The NES involves an essential cubic restoring force and a linear damping force. The analysis is achieved applying complexification-averaging method. The resulting slow-flow model is finally analyzed using multiple scale approach. Four steady-state responses corresponding to complete suppression, partial suppression through strongly modulated response, partial suppression through periodic response and no suppression of the GR are highlighted. An algorithm based on simple criterions is developed to predict these steady-state response regimes. Numerical simulations of the complete system confirm this analysis of the slow-flow dynamics. A parametric analysis of the influence of the NES damping coefficient and the rotor speed on the response regime is finally proposed.
 Keywords
helicopter ground resonance;passive control;nonlinear energy sink;relaxation oscillations;strongly modulated response;
 Language
English
 Cited by
1.
Mode coupling instability mitigation in friction systems by means of nonlinear energy sinks: Numerical highlighting and local stability analysis, Journal of Vibration and Control, 2017, 107754631770710  crossref(new windwow)
2.
Passive suppression of helicopter ground resonance using nonlinear energy sinks attached on the helicopter blades, Journal of Sound and Vibration, 2017, 392, 41  crossref(new windwow)
 References
1.
Bellet, R., Cochelin, B., Herzog, P. and Mattei, P.O. (2010), "Experimental study of targeted energy transfer from an acoustic system to a nonlinear membrane absorber", J. Sound Vib., 329, 2768-2791. crossref(new window)

2.
Bergeot, B., Bellizzi, S. and Cochelin, B. (2016), "Analysis of steady-state response regimes of a helicopter ground resonance model including a non-linear energy sink attachment", Int. J. Nonlin. Mech., 78, 72-89. crossref(new window)

3.
Bramwell, A.R.S., Balmford, D. and Done, G.T.S. (2001), Bramwell's helicopter dynamics.

4.
Caughey, T.K. and O'Kelly, M.E.J. (1963), General theory of vibration of damped linear dynamic systems, Dynamics Laboratory, California Institute of Technology, Pasadena.

5.
Coleman, R.P. and Feingold, A.M. (1958), "Theory of self excited mechanical oscillations of helicopter rotor with hinged blades", Technical Report, NACA Report 1351.

6.
Done, G.T.S. (1974), "A simplified approach to helicopter ground resonance", Aeronaut. J., 78(761), 204-208.

7.
Gendelman, O., Vakakis, A., Bergman, L. and McFarland, D. (2010), "Asymptotic analysis of passive nonlinear suppression of aeroelastic instabilities of a rigid wing in subsonic flow", SIAM J. Appl. Math., 70(5), 1655-1677. crossref(new window)

8.
Gendelman, O.V. and Bar, T. (2010), "Bifurcations of self-excitation regimes in a Van der Pol oscillator with a nonlinear energy sink", Physica D., 239(3-4), 220-229. crossref(new window)

9.
Grasman, J. (1987), Asymptotic Methods for Relaxation Oscillations and Applications, Volume 63, Applied Mathematical Sciences, Springer-Verlag.

10.
Johnson, W. (1994), Helicopter theory, Dover publications, inc.

11.
Krysinski, T. and Malburet, F. (2009), Instabilite mecanique: controle actif et passif, Lavoisier.

12.
Lee, Y.S., Vakakis, A.F., Bergman, L.A., McFarland, D.M. and Kerschen, G. (2007a), "Suppression aeroelastic instability using broadband passive targeted energy transfers, part 1: theory", AIAA J., 45(3), 693-711. crossref(new window)

13.
Lee, Y.S., Vakakis, A.F., Bergman, L.A., McFarland, D.M. and Kerschen, G. (2007b), "Suppression aeroelastic instability using broadband passive targeted energy transfers, part 2: experiments", AIAA J., 45(3), 2391-2400. crossref(new window)

14.
Leissa, A.W. (1974), "On a curve veering aberration (ZAMP)", J. Math. Phys., 25, 99-111.

15.
Luongo, A. and Zulli, D. (2014), "Aeroelastic instability analysis of nes-controlled systems via a mixed multiple scale/harmonic balance method", J. Vib. Control, 20(13), 1985-1998. crossref(new window)

16.
Manevitch, L. (1999), "Complex representation of dynamics of coupled nonlinear oscillators, Eds. Uvarova, L., Arinstein, A. and Latyshev, A., Mathematical Models of Non-Linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media, Springer US.

17.
Nayfeh, A.H. (2011), Introduction to perturbation techniques, Wiley VCH.

18.
Sanches, L., Michon, G., Berlioz, A. and Alazard, D. (2012), "Parametrically excited helicopter ground resonance dynamics with high blade asymmetries", J. Sound Vib., 331(16), 3897-3913. crossref(new window)

19.
Seydel, R. (2010), Practical Bifurcation and Stability Analysis, Volume 5, Interdisciplinary Applied Mathematics, Springer, 3ieme Edition.

20.
Starosvetsky, Y. and Gendelman, O.V. (2008), "Strongly modulated response in forced 2dof oscillatory system with essential mass and potential asymmetry", Physica D., 237(13), 1719-1733. crossref(new window)

21.
Vakakis, A. and Gendelman, O. (2001), "Energy pumping in nonlinear mechanical oscillators: Part II-Resonance capture", J. Appl. Mech., 68, 42-48. crossref(new window)

22.
Vakatis, A.F., Gendelman, O.V., Bergman, L.A., McFarland, D.M., Kerschen, G. and Lee, Y.S. (2008), Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems, Springer-Verlag, Berlin, New York.