Browse > Article
http://dx.doi.org/10.12989/aas.2016.3.3.271

Passive suppression of helicopter ground resonance instability by means of a strongly nonlinear absorber  

Bergeot, Baptiste (INSA Centre Val de Loire, Universite Francois Rabelais de Tours)
Bellizzi, Sergio (LMA, CNRS UPR7051, Aix-Marseille Univ.)
Cochelin, Bruno (LMA, CNRS UPR7051, Aix-Marseille Univ.)
Publication Information
Advances in aircraft and spacecraft science / v.3, no.3, 2016 , pp. 271-298 More about this Journal
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;
Citations & Related Records
연도 인용수 순위
  • Reference
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
14 Leissa, A.W. (1974), "On a curve veering aberration (ZAMP)", J. Math. Phys., 25, 99-111.
15 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.   DOI
16 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.   DOI
17 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.
18 Nayfeh, A.H. (2011), Introduction to perturbation techniques, Wiley VCH.
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.   DOI
21 Vakakis, A. and Gendelman, O. (2001), "Energy pumping in nonlinear mechanical oscillators: Part II-Resonance capture", J. Appl. Mech., 68, 42-48.   DOI
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.