Flutter is the state of turbulent vibrations of a lifting surface in coupled bending and torsional direction which ultimately can lead to catastrophic failures and destruction of the whole airplane structure. When a lifting surface is placed in an unsteady fluid flow, it will experience disturbances over the surface area. These disturbances have a specific frequency at which they vibrate. At low initial speeds, the oscillations are damped by the structural stiffness. Hence, the oscillations does not go violent and are under control. This is a normal state and needs no special attention.

As the fluid flow speed increases with respect to the lifting surface, the oscillation frequency increases and the rate of structural damping decreases gradually which results in a high but steady amplitude oscillations of the lifting surface. This state is called the Zero-damping state as the structural damping reduces to zero and this speed of fluid flow is called Critical flutter speed.

At this state, an oscillation can just maintain itself with a steady amplitude. Above the critical flutter speed, a small disturbance in the fluid flow can trigger to initiate an oscillation of great violence. In other words, we can describe the flutter phenomenon is three stages. Stage I is when the speed is less than the critical flutter speed and the structural damping is positive, hence, the oscillations die out after a period of time. Stage II is when the speed is equal to the critical flutter speed and the structural damping is near to 0+ or 0 (zero).

At this stage, the oscillations neither grow nor die, the lifting surface oscillates with a steady amplitude. Stage III is when the fluid flow speed becomes more than the critical flutter speed and the structural damping becomes positive, so as to support the oscillations to become more violent. This state is called flutter and its analysis is the main objective of this paper. There is more than one reason for the occurrence of flutter. Flutter phenomenon is also a result of coupling of several degrees of freedom, which is also an essential feature of flutter. The past experiments proves that most of the times the bending deformations across the span are in phase with one another. Similarly, the torsional movements across the span are in phase, but the bending is significantly out of phase from the torsional deformation.

This phase difference is responsible for occurrence of the flutter phenomenon. An airplane wing, as a deformable elastic body, has infinitely many degrees of freedom. But we can describe the airplane’s elastic deformation in any chordwise section using only two degrees of freedom with sufficient accuracy: the vertical deflection at any reference point and the angle of rotation of a point, i.e., the bending and torsional deformations, respectively.