and therefore the solutions are of type: , representing motions for which: Damping [rad/sec] Radial frequency [rad/sec] Stability of motion is indicated by the value of : Unstable (increasing amplitude) Neutral (constant amplitude) Stable (decreasing amplitude) Some possible flutter solutions are given in the next table, showing: Condition of coefficients Type of solution and physical meaning Classification into stability categories >0 >0 >0 <0 >0 >0 <0 or >0 <0 or or , , , , , , Type of motion Harmonic: Aperiodic: Aperiodic: Oscillatory: 2 positive freq. 2 diverging 1 diverging 1 div. pos. freq. 2 negative 2 converging 1 converging 1 conv. pos. freq. freq. Harmonic: 1 div. neg. freq. 1 positive freq. 1 conv. neg. freq. 1 negative freq. Type of instability Neutral Divergence Divergence Flutter Category I III IV II Types of instabilities of a typical airfoil (steady aerodynamic model) The analysis of a two degree of freedom system yields to a more realistic situation and includes additional parameters are essential for a flutter boundary discussion. Unsteady Aerodynamic Model The equations of motions are, in this case, written as: As previously done, the motion is assumed to be harmonic and represented by
and therefore the solutions are of type: , representing motions for which: Damping [rad/sec] Radial frequency [rad/sec] Stability of motion is indicated by the value of : Unstable (increasing amplitude) Neutral (constant amplitude) Stable (decreasing amplitude) Some possible flutter solutions are given in the next table, showing: Condition of coefficients Type of solution and physical meaning Classification into stability categories >0 >0 >0 <0 >0 >0 <0 or >0 <0 or or , , , , , , Type of motion Harmonic: 2 positive freq. 2 negative freq. Aperiodic: 2 diverging 2 converging Aperiodic: 1 diverging 1 converging Harmonic: 1 positive freq. 1 negative freq. Oscillatory: 1 div. pos. freq. 1 conv. pos. freq. 1 div. neg. freq. 1 conv. neg. freq. Type of instability Neutral Divergence Divergence Flutter Category I III IV II Types of instabilities of a typical airfoil (steady aerodynamic model) The analysis of a two degree of freedom system yields to a more realistic situation and includes additional parameters are essential for a flutter boundary discussion. Unsteady Aerodynamic Model The equations of motions are, in this case, written as: As previously done, the motion is assumed to be harmonic and represented by
Appunti_flu_03.docx