Analysis of biomechanical passive synergistic vibration reduction inspired by the structure, morphology, nano-mechanics of the beetles' hindwing.

Using scanning electron microscopy (SEM), a small animal imaging system, and biological tissue sections, the relationships between the flapping vibrations in the hindwings of Trypoxylus dichotomus and their morphology, structure, and hemolymph dynamics were investigated. Based on these findings, a three-degree-of-freedom (3-DOF) model incorporating nano-mechanical properties was developed to investigate spanwise passive synergistic vibration reduction (PSVR) in the hindwing elements. To ensure precision, the Runge-Kutta and incremental harmonic balance (IHB) methods were employed for both solving and comparing solutions. Analysis of the spanwise force (F) signals confirmed the validity of the PSVR model. Parametric analysis revealed that reducing system mass and stiffness increased the resonance amplitude while shifting the resonance frequency in the opposite direction. The resonance frequency and flexible deformation amplitude of the hindwing system could be controlled by adjusting mass and stiffness within the synergistic framework. The mass and damping of the wing base, along with the stiffness of the wing membrane, were identified as critical factors in the system. This model provides valuable insights into the PSVR mechanism, potentially informing the design and manufacture of bionic flexible flapping wings.