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仿节肢动物肢体构型的M型低频隔振结构设计及其动力学机理研究

蓝春波 贾洁 汪洋 王烁 张璐

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仿节肢动物肢体构型的M型低频隔振结构设计及其动力学机理研究

蓝春波, 贾洁, 汪洋, 王烁, 张璐

Dynamic Analysis of an Arthropod-Limb-Inspired M-Shaped Structure for Low-Frequency Vibration Isolation

Lan Chunbo, Jia Jie, Wang Yang, Wang Shuo, Zhang Lu
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  • 蜘蛛、螳螂等节肢动物能够在晃动的蛛网或树叶上保持身体的稳定性,其类“M”型肢体结构的作用不可忽视。受此启发,本文提出了一种基于节肢动物肢体结构的仿生M型低频隔振结构。首先,提出了仿生M型低频隔振结构的设计方法,并建立了其动力学模型。通过对其等效刚度、准零刚度范围等静态特性的对比分析,发现仿生M型结构的非线性刚度能够有效拓宽准零刚度范围。运用谐波平衡法进行了近似求解,得到了其频率响应特性,并分析了其频率和幅值分岔动力学特性。通过与经典三弹簧准零刚度结构对比,发现M型仿生结构能够有效降低隔振频率,并能降低隔振频带内的传递率。最后,研究了M型仿生结构的几何形状对其隔振性能的影响规律,结果表明,类似蜘蛛肢体的扁平状M型结构具有更低的隔振频率,更好的低频隔振效果。
    Arthropods, including spiders and mantises, are capable of maintaining their body stability on shaking surfaces, such as spiderwebs or leaves. This impressive stability can be attributed to the specific geometry of their limbs, which exhibit an M-shaped structure. Inspired by this geometry, this paper proposes an arthropod-limb-inspired M-shaped structure for low-frequency vibration isolation. First, the design methodology of the M-shaped quasi-zero-stiffness (QZS) structure is presented. A static analysis of potential energy, restoring force, and equivalent stiffness is conducted. It is revealed that the M-shaped structure enables a horizontal linear spring to generate nonlinear stiffness in the vertical direction. More importantly, this nonlinear stiffness effectively compensates for the negative stiffness in large-displacement responses, thereby achieving a wider quasi-zero-stiffness region compared to the conventional three-spring-based QZS structure. Subsequently, the harmonic balance method was employed to derive approximate analytical solutions for the M-shaped QZS structure, which were well validated through numerical simulation. A comparison between the proposed M-shaped QZS structure and the conventional three-spring-based QZS structure was performed. Results show that the M-shaped QZS structure is advantageous for reducing both the cut-in isolation frequency and the resonance frequency. In particular, under large excitation or small damping conditions, the performance improvement of the M-shaped QZS structure in terms of reducing the resonance frequency and maximum response becomes more pronounced. The underlying mechanism behind this feature is primarily attributed to the expanded QZS region induced by the M-shaped structure. Lastly, since the M-shaped structures vary among different arthropods, the effect of the geometry of M-shaped structures on low-frequency vibration performance was investigated. Interestingly, a trade-off between vibration isolation performance and loading mass was observed. As the M-shaped structure becomes flatter, the QZS region expands, and both the cut-in isolation frequency, the resonance frequency/peak, and the loading mass decrease. This occurs because a flatter M-shaped structure leads to a reduction in the equivalent stiffness generated by the horizontal stiffness. Consequently, while the loading mass capacity decreases, the low-frequency vibration isolation performance is enhanced. This novel finding provides a reasonable explanation for why most arthropods possess many pairs of limbs, allowing the loading mass to be distributed and enabling excellent low-frequency vibration isolation to be achieved simultaneously.
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