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Digital Study of a Stability Analogy

Published online by Cambridge University Press:  04 July 2016

B. S. Thornton  and
T. M. Park
B. S. Thornton
Affiliation:
Honeywell EDP, Sydney, Australia
T. M. Park
Affiliation:
ICT, Bracknell
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Extract

An investigation has been made into the stability of compressor blade flutter in separating flow in the presence of external perturbations. The fluttering blade is an example of a hysteretic system governed by a non-linear difference-differential equation for which an analytical approach is not possible and for which the authors originally proposed this new treatment. For design purposes a digital computer has been used to produce stability diagrams under specified conditions including blade torsion. The solution for the response is also available if required. The method involves forming the non-linear feedback analogue to the blade system and which has behaviour governed by the same equation as that studied. The stability is then studied on a digital computer in the presence of small external perturbations by means of a dual input describing function applied to the analogous feedback system with consideration given to the aerodynamic phase lag involved and initially small blade torsional motion.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 71 , Issue 680 , August 1967 , pp. 576 - 579
Copyright
Copyright © Royal Aeronautical Society 1967

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References

1.Park, T. M. and Thornton, B. S. The Stability of Non- Linear Difference—Differential Equations in Aero dynamics. Proceedings First Australian National Computer Conference, Paper B19.2, Sydney, May 1960.Google Scholar
2.Thornton, B. S.Compressor Blade Flutter in Jet Engines. PhD Thesis, School of Mathematics, University of New South Wales, 1960.Google Scholar
3.Holder, D. W.The Transonic Flow Past Two-Dimensional Aerofoils. Second Reynolds-Prandtl Lecture. Journal of the Royal Aeronautical Society, Vol 68, p 515, 1964.CrossRefGoogle Scholar
4.Sisto, F.Stall Flutter in Cascades. Journal of Aeronautical Sciences, Vol 20, p 598, 1953.Google Scholar
5.Bhatt, S. J. and Hsu, C. S.Stability Criteria for Second-Order Dynamical Systems with Time Lag. Journal of Applied Mechanics, Vol 33, Series E, No 1, p 113, 1966.Google Scholar
6.Bhatt, S. J. and Hsu, C. S.Stability Charts for Second- Order Dynamical Systems with Time Lag. Ibid, p 119.Google Scholar
7.West, J. C, Douce, J. L. and Livesley, R. K.The Dual Input Describing Function and its Use in the Analysis of Non-Linear Systems. Proceedings Institute of Electrical Engineers, Paper No 1877M, p 463, 1955.Google Scholar
8.Tustin, A.Method of Analysing the Behaviour of Linear Systems in Terms of Time Series. Journal Institute of Electrical Engineers, Vol 94, Part Ila, p 130, 1947.Google Scholar
9.Stephenson, J. M.Measurement of the Profile Drag of Compressor and Turbine Cascades and the Effect of Wakes in Exciting Vibration. Journal of the Royal Aeronautical Society, Vol 57, p 722, 1953.Google Scholar