Purdue Aeroelasticity AAE 556 - Aeroelasticity Flutter-Lecture 20 Purdue Aeroelasticity
Quasi-steady flutter with a typical section vibration idealization Flutter is a self-excited, dynamic, oscillatory instability requiring the of motion and interaction between two different modes an external energy supply Quasi-steady aerodynamic loads capture some dynamic effects of the lift force, but ignore lags between motion and developing forces and moments Assumed harmonic motion Purdue Aeroelasticity
Flutter and frequency merging Purdue Aeroelasticity
Purdue Aeroelasticity What we are looking for Purdue Aeroelasticity
Free vibration with the air on looking for clumps of parameters Purdue Aeroelasticity
Purdue Aeroelasticity The prize Remember what the bars mean. Purdue Aeroelasticity
Calculate the determinant what do you hope to discover? 2b c.g. shear center aero center Purdue Aeroelasticity
Quadratic equation for frequency squared Purdue Aeroelasticity
The A, B terms are airspeed dependent Purdue Aeroelasticity
Divergence is a special case set then Purdue Aeroelasticity
Purdue Aeroelasticity Divergence Purdue Aeroelasticity
Solution for natural frequencies When the airspeed is zero then these eigenvalues are real and distinct. They stay that way as airspeed increases. That means our original assumption of harmonic (sinusoidal) motion is correct. Purdue Aeroelasticity
Purdue Aeroelasticity The transition point between stability and instability for this idealization is frequency merging Two solutions with the same frequencies instability Purdue Aeroelasticity
Frequency depends on airspeed Purdue Aeroelasticity
Transition to instability ????? Purdue Aeroelasticity
Purdue Aeroelasticity Two roots Purdue Aeroelasticity
Purdue Aeroelasticity Frequency merging Purdue Aeroelasticity
Solution for frequency When the airspeed is zero then these eigenvalues are real and distinct - they also depend on airspeed ... Purdue Aeroelasticity
Purdue Aeroelasticity When the frequencies are real and distinct then no energy is input or extracted over one cycle Mode shapes are important Purdue Aeroelasticity