On the natural frequencies and mode shapes of dragonfly wings

A base-excitation modal testing technique is adopted to measure the natural frequencies and mode shapes of dragonfly wings severed from thoraxes. The severed wings are glued onto the base of a shaker, which is capable of inducing translational motion in the lateral direction of the wing plane. Photonic probes are used to measure the displacement history of the shaker base and the painted spots of the wing simultaneously. A spectrum analyzer is employed to calculate the frequency response functions, from which the natural frequencies and the associated mode shapes of the wing structure can be extracted. Our experimental results show that the fundamental natural frequency of dragonfly wings is in the order of 170 Hz when it is clamped at the wing base. The average flapping frequency 27 Hz of dragonflies is about 16% of the fundamental natural frequency. At this frequency ratio, the inertial force of the wing is negligible compared to the elastic force. In other words, the wing deformation during flapping flight is solely due to the balance between the external aerodynamic force and the elastic force of the wing structure. The wing structures are generally lightly damped, with damping ratio in the order less than 5%.