One degree of Freedom Flutter To discuss some simple flutter analysis calculations we will present the of one and two degrees of freedom. Both examples are referred to a rigid two-dimensional airfoil which in the first case (SDOF) is permitted only to rotate in pitch about a specific reference point, and the plunge degree of freedom is equal to zero as shown in figure: Fig. 2.1 Geometry of the wing section showing the pitch degree of freedom – The system equations of motion reduce to one equation which can be written as: where moment of inertia around the point P torsional stiffness around the point P aerodynamic pitching moment around the point P angle of attack (degree of freedom) As generally assumed in a classical flutter analysis, the motion of the system is considered to be harmonic as and the subsequent aerodynamic pitching moment is harmonic too: where with = reduced frequency = = Mach number of the free airstream Substituting expressions into the equation of motion we get the algebraic equation Introducing the natural frequency of the system at zero airspeed and simplifying , one obtain The values of should be assumed to be for the solution of the previous equation. The unknown parameters, describing the flight condition, are . These fours unknowns must be determined from the single algebraic previous equation. The unsteady aerodynamic coefficient is a complex number may be written as:
One degree of Freedom Flutter To discuss some simple flutter analysis calculations we will present the of one and two degrees of freedom. Both examples are referred to a rigid two-dimensional airfoil which in the first case (SDOF) is permitted only to rotate in pitch about a specific reference point, and the plunge degree of freedom is equal to zero as shown in figure: Fig. 2.1 – Geometry of the wing section showing the pitch degree of freedom The system equations of motion reduce to one equation which can be written as: where moment of inertia around the point P torsional stiffness around the point P aerodynamic pitching moment around the point P angle of attack (degree of freedom) As generally assumed in a classical flutter analysis, the motion of the system is considered to be harmonic as and the subsequent aerodynamic pitching moment is harmonic too: where with = reduced frequency = = Mach number of the free airstream Substituting expressions into the equation of motion we get the algebraic equation Introducing the natural frequency of the system at zero airspeed and simplifying , one obtain The values of should be assumed to be for the solution of the previous equation. The unknown parameters, describing the flight condition, are . These fours unknowns must be determined from the single algebraic previous equation. The unsteady aerodynamic coefficient is a complex number may be written as:
Appunti_flu_03.docx