Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-06T19:48:55.341Z Has data issue: false hasContentIssue false
  • English
  • Français

Laplace-domain approximation to the transfer functions of a rotor blade in forward flight

Published online by Cambridge University Press:  04 July 2016

F. Nitzsche
F. Nitzsche*
Affiliation:
Department of Mechanical and Aerospace Engineering, Carleton University, Ottawa, Ontario, Canada
Get access Rights & Permissions [Opens in a new window]

Abstract

A continuous frequency domain method with roots on the classic Hill’s determinant analysis is presented to approximate the time-varying characteristics of a linear periodic system. The method is particularly useful to derive a time-invariant equivalent form of the time-varying aeroelastic problem of a rotor blade in forward flight. The proposed technique allows methodology usually employed in fixed wing aircraft to obtain closed-loop control laws be extended to rotary wings. The method is first validated solving Mathieu’s equation. Next, the two-degree-of-freedom (flap bending and torsion) problem of rotating beam subject to unsteady and incompressible aerodynamics in forward flight is solved in the laplace domain. As a demonstration of the proposed method, the transfer functions in the ‘s’ plane between a sudden and uniformly distributed input pressure perturbation applied along the beam and the output response of the two elastic degrees of freedom considered are obtained at a set of local sections.

Type
Research Article
Information
The Aeronautical Journal , Volume 105 , Issue 1047 , April 2001 , pp. 233 - 240
Copyright
Copyright © Royal Aeronautical Society 2002 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Nitzsche, F.A. New individual blade control approach to attenuate rotor vibration, Proceedings of the 22nd European Rotorcraft Forum, RAeS. UK, 1996, Paper 8, (I).Google Scholar
2. Lehman, L.L. Hybrid state vector methods for structural dynamic and aeroelastic boundary value problems, NASA CR-3591, 1982.Google Scholar
3. Friedmann, P.P. Arbitrary motion unsteady aerodynamics and its application to rotary-wing aeroelasticity, J Fluids and Structures, 1987,1 ,pp 71–93.Google Scholar
4. Isaacs, R. Aerofoil theory for flows of variable velocity, J Aeronautical Sciences, 1945, 12, (1), pp 113–117.Google Scholar
5. Richards, J.A. Analysis of Periodically Time-Varying Systems, Springer-Verlag, 1983, pp 57–68.Google Scholar
6. Erdélyi, A. Über die Integration der Mathieschen Differentialgleichung durch Laplacesche Integrale, Mathematische Zeitschrift, 1936, 41, pp 653–664.Google Scholar
7. Erdelyi, A. Bemerkungen zur Integration der Mathieuschen Differentialgleichung durch Laplacesche Integrale, Compositio Mahematica, 1938, 5, pp 435–441.Google Scholar
8. Spettstösser, W.R., Niesl, G., Cenedese, F., Nitti, F. and Papanikas, D.G. Experimental results of the European HELINOISE aeroacoustic rotor test in the DNW, 19th European Rotorcraft Forum, Cernobbio, Italy, 14-–6 September 1993, Paper B8.Google Scholar
9. Vepa, R. Finite-state modeling of aeroelastic systems, NASA CR-2779, 1977.Google Scholar
10. Karpel, M. Design for active flutter suppression and gust alleviation using state-space aeroelastic modeling, J Aircr, 1982, 19, (3), pp 221-227.Google Scholar
11. Gennaretti, M., Corbelli, A. and Mastroddi, F. A comparison among some aeroelastic models for the stability analysis of a flap-lag-torsion helicopter rotor in hover, 26th European Rotorcraft Forum, The Hague, The Netherlands, 26-29 September 2000. Paper 68.Google Scholar
12. Johnson, W. Helicopter Theory, Princeton University Press, 1980, pp 492–498.Google Scholar
13. McLachlan, N.W. Theory and Applications of Mathieu Functions, Oxford University Press, New York, 1947, pp 128–129.Google Scholar
14. McLachlan, N.W. Theory and Applications of Mathieu Functions, Oxford University Press, New York, 1947, pp 58–59.Google Scholar