Measurement of natural frequencies and mode shapes of transparent insect wings using common-path ESPI

Abstract

In this study, a common-path electronic speckle pattern interferometry system which upholds the natural property of transparency of insect’s wings has been developed to measure the wings’ natural frequencies and mode shapes for the first time. A novel base-exciting method was designed to enable the simultaneous application of sinusoidal and static forces to excite wings and introduce an additional phase. The moiré effect induced by the amplitude modulation was employed to accurately recognize the resonance state. Subsequently, the mode shapes were visualized by phase-shifting and real-time frame subtraction. Eight pairs of forewings from cicadas were investigated. The first three order natural frequencies of the wings are approximately 145 Hz, 272 Hz and 394 Hz, respectively, which are dispersed to prevent modal coupling. The cambered mode shapes exhibit a strongly spanwise-chordwise anisotropy flexural stiffness distribution, generally dominated by bending and twisting deformation. The details of the high-order mode shapes show that the tip exhibits distinct deformation, indicating more flexibility to cope with external impact load, and the nodal lines usually comply with the direction of the wing veins in higher modes, substantiating the fact that the veins play an important role as stiffeners of the membrane. The results are in excellent agreement with the dynamic performance of previous studies, which will potentially affect a broader community of optical measurement specialists and entomologists to enhance our understanding of time-averaged interferograms and insect flights.