Estimation of the Hopf bifurcation point for aeroelastic systems

The estimation of the Hopf bifurcation point is an important prerequisite f or the non-linear analysis of non-linear instabilities in aircraft using th e classical normal form theory. For unsteady transonic aerodynamics, the ae roelastic response is frequency-dependent and therefore a very costly trial -and-error and iterative scheme, frequency-matching, is used to determine f lutter conditions. Furthermore, the standard algebraic methods have usually been used for systems not bigger than two degrees of freedom and do not ap pear to have been applied for frequency-dependent aerodynamics. In this stu dy, a procedure is developed to produce and solve algebraic equations for a ny order aeroelastic systems, with and without frequency-dependent aerodyna mics, to predict the Hopf bifurcation point. The approach performs the comp utation in a single step using symbolic programming and does not require tr ial and error and repeated calculations at various speeds required when usi ng classical iterative methods. To investigate the validity of the approach , a Hancock two-degrees-of-freedom aeroelastic wing model and a multi-degre e-of-freedom cantilever wind model were studied in depth. Hancock experimen tal data was used for curve fitting the unsteady aerodynamic damping term a s a function of frequency. Fairly close agreement was obtained between the analytical and simulated aeroelastic solutions with and without frequency-d ependent aerodynamics. (C) 2001 Academic Press.