A. SEDAGHAT, J. E. COOPER, A. Y. T. LEUNG AND J. R. WRIGHT, ESTIMATION OF THE HOPF BIFURCATION POINT FOR AEROELASTIC SYSTEMS, Journal of Sound and Vibration (2001) 248(1), 31-42.
Journal of Sound and Vibration (2001) 248(1), 31-42
ESTIMATION OF THE HOPF BIFURCATION POINT FOR AEROELASTIC SYSTEMS
A. SEDAGHAT, J. E. COOPER, A. Y. T. LEUNG AND J. R. WRIGHT
Dynamics & Aeroelasticity Group, Manchester School of Engineering, Manchester M13 9P¸, England.
(Received 16 November 2000, and in ,nal form 22 February 2001)
The estimation of the Hopf bifurcation point is an important prerequisite for the
non-linear analysis of non-linear instabilities in aircraft using the classical normal
form theory. For unsteady transonic aerodynamics, the aeroelastic response is
frequency-dependent and therefore a very costly trial-and-error and iterative scheme,
frequency-matching, is used to determine #utter conditions. Furthermore, the standard
algebraic methods have usually been used for systems not bigger than two degrees of
freedom and do not appear to have been applied for frequency-dependent aerodynamics. In
this study, a procedure is developed to produce and solve algebraic equations for any order
aeroelastic systems, with and without frequency-dependent aerodynamics, to predict the
Hopf bifurcation point. The approach performs the computation in a single step using
symbolic programming and does not require trial and error and repeated calculations at
various speeds required when using classical iterative methods. To investigate the validity of
the approach, a Hancock two-degrees-of-freedom aeroelastic wing model and
a multi-degree-of-freedom cantilever wind model were studied in depth. Hancock
experimental data was used for curve "tting the unsteady aerodynamic damping term as
a function of frequency. Fairly close agreement was obtained between the analytical and
simulated aeroelastic solutions with and without frequency-dependent aerodynamics.