蜻蜓翅膀的自然頻率與振形量測

Abstract

蜻蜓翅膀的自然頻率與振形量測 摘要

本文以基台激振法為理論基礎，進行對蜻蜓翅膀的模態分析。本實驗將蜻蜓翅膀從身體切下，以垂直翅膀平面方向的運動方式黏於激振器上，利用頻譜分析儀中的Swept Sine Measurements功能，使激振器在100Hz至500Hz的頻率下連續激振。再以光纖感測器探頭量取激振器與翅膀銀漆上的瞬間振動位移。藉著頻譜分析儀的運算，可以得到頻率響應函數，再由頻率響應函數可進一步得到蜻蜓翅膀的自然頻率與相對應的振動模態。 由本實驗結果得知當蜻蜓翅膀黏於激振器時，翅膀的基頻約在170Hz上下。而蜻蜓飛行時的拍翅頻率(27Hz)約為其基頻的16%，所以當蜻蜓拍翅時，翅膀本身的慣性力相較於彈性力是可忽略的。換句話說，蜻蜓飛行時翅膀的變形僅與外在的空氣動力有關，並可視為準靜態的變形。而相對應的振動模態則包含彎曲及扭轉的變形。

On the Natural Frequencies and Mode Shapes of Dragonfly Wings Abstract A base excitation modal testing technique is adopted to measure the natural frequencies and mode shapes of dragonfly wings severed from the torsos. 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. The excitation frequency of the shaker is set to sweep from 100 to 500 Hz. A spectrum analyzer is responsible for calculating the frequency response functions, from which we can extract the natural frequencies and the associated mode shapes of the wing structure. 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 frequency. Therefore, the inertial force of the wing is negligible compared to the elastic force when the dragonfly flaps its wings. In other words, the wing deformation is solely due to external aerodynamic force and can be considered as quasi-static. The corresponding mode shapes contain both bending and twisting deformations.