Flapping at Resonance: Measuring the Frequency Response of the Hymenoptera Thorax

Insects with asynchronous flight muscles are believed to flap at the fundamental frequency of their thorax or 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 thorax has not been measured via vibration testing. Here, we measure the linear frequency response function (FRF) of several Hymenoptera (Apis mellifera, Polistes dominula, Bombus huntii) thoraxes about their equilibrium states 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 m, thorax fundamental frequencies in all specimens approximately 50-150% higher than reported wingbeat frequencies. We suspect that the measured fundamental frequencies are higher in the experiment than during flight due to experimental boundary conditions that stiffen the thorax. Thus, our results corroborate the idea that some insects flap at the fundamental frequency of their thorax. Next, we compress the thorax between 100 - 300 m in 50 m intervals to assess the sensitivity of the fundamental frequency to geometric modifications. For all insects considered, the thorax fundamental frequency increased nearly monotonically with respect to level of compression. This implies that the thorax behaves a nonlinear hardening spring, which we confirmed via static force-displacement testing. Hardening behavior may provide a simple mechanism for the insect to adjust wingbeat frequency, and implies the thorax may behave as a nonlinear Duffing oscillator excited at large amplitude. The Duffing oscillator exhibits amplitude-dependent resonance and may serve as a useful model to increase the flapping frequency bandwidth of small resonant-type flapping wing micro air vehicles.