Insects with asynchronous flight muscles are believed to flap at the effective fundamental frequency of their thorax-wing system. Flapping in this manner leverages the natural elasticity of the thorax to reduce the energetic requirements of flight. However, to the best of our knowledge, the fundamental frequency of the insect wing-muscle-thorax system has not been measured. Here, we measure the linear frequency response function (FRF) of honeybee Apis mellifera thoraxes about their equilibrium state in order to determine their fundamental frequencies. FRFs relate the input force to output acceleration at the insect tergum and are acquired via a mechanical vibration shaker assembly. When compressed 50 μm, the thorax fundamental frequency averaged across all subjects was about 50% higher than reported wingbeat frequencies. We suspect that the measured fundamental frequencies are higher in the experiment than during flight due to boundary conditions and posthumous muscle stiffening. Next, we compress the thorax between 100-300 μm in 50 μm intervals to assess the sensitivity of the fundamental frequency to geometric modifications. For all specimens considered, the thorax fundamental frequency increased nearly monotonically with respect to level of compression. This implies that the thorax behaves as a nonlinear hardening spring when subject to large displacements, which we confirmed via static force-displacement testing. While there is little evidence that insects utilize this non-linearity during flight, the hardening characteristic may be emulated by small resonant-type flapping wing micro air vehicles to increase flapping frequency bandwidth. Overall, methods established through this work provide a foundation for further dynamical studies on insect thoraxes moving forward.

中文翻译：

---

测量蜜蜂胸部的频率响应。

具有异步飞行肌肉的昆虫被认为会以其胸翅系统的有效基频拍动。以这种方式拍打可利用胸部的自然弹性来减少飞行的精力需求。然而，据我们所知，昆虫翼-肌肉-胸部系统的基本频率尚未测量。在这里，我们测量蜜蜂蜜蜂胸部的线性频率响应函数（FRF）关于它们的平衡状态，以确定它们的基本频率。FRF将输入力与昆虫尾端的加速度相关联，并通过机械振动筛组件获得。当压缩50μm时，所有受试者的平均胸廓基频均比报道的机翼拍频高约50％。由于边界条件和死后肌肉僵硬，我们怀疑在实验中测得的基频比飞行中更高。接下来，我们以50μm的间隔在100-300μm之间压缩胸腔，以评估基本频率对几何修改的敏感性。对于所有考虑的标本，胸部基本频率相对于压缩水平几乎单调增加。这意味着当受到大位移时，胸部表现为非线性硬化弹簧，我们通过静态力-位移测试证实了这一点。尽管几乎没有证据表明昆虫在飞行过程中利用了这种非线性，但硬化特性可以通过小型共振型扑翼微型航空飞行器来模拟，以增加扑翼频率带宽。总体，