This paper develops a geometrically nonlinear mathematical model of a flexible cantilevered beam hosting a guided axially elastic tendon. The model is intended as an enabling tool to explore the guided tendon-based dynamic enhancement methods in application to highly flexible and lightweight structures. To both validate the model and to generate further insights, an experiment-guided study is performed on a beam-tendon configuration. Uniquely, this is done with moderately large beam deformations used to exercise nonlinearity. The model-based study of the problem identifies and reflects on the individual stiffness-modulating terms corresponding to various geometrical and axial elasticity-driven mechanisms. The susceptibility to these individual modulating mechanisms is shown to vary between different groups of modes. These are systematically identified using contrasting frequency variations created by the different mechanisms. The second novel aspect of this research is the treatment of the resistive effects posed by the guides on the tendon’s axial movement. It is shown that the progressive locking of the tendon’s motion with increased guide impedance results in higher extents of stiffening due to the segmented activation of the tendon’s elasticity. It is further demonstrated that the effective tailoring of the impedance posed by the guides can be used to generate dynamically optimal conditions. This is illustrated for the specific case of modal damping maximisation, assuming guide-impedance originating in the form of viscous damping. Given these insights, this research recognises potential extensions of the axially activated tendon for vibration suppression applications.

中文翻译：

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通过引导的轴向弹性筋对几何非线性梁进行动态增强


本文开发了一个柔性悬臂梁的几何非线性数学模型，该模型承载着引导的轴向弹性肌腱。该模型旨在作为一种使能工具，探索基于导向肌腱的动态增强方法在高柔性和轻质结构中的应用。为了验证模型并产生进一步的见解，对梁-肌腱配置进行了实验指导的研究。独特的是，这是通过用于练习非线性的中等大梁变形来实现的。基于模型的问题研究识别并反映了对应于各种几何和轴向弹性驱动机构的各个刚度调制项。对这些单独的调制机制的敏感性在不同的模式组之间有所不同。这些是利用不同机制产生的对比频率变化系统地识别出来的。这项研究的第二个新颖方面是处理导向器对肌腱轴向运动造成的阻力效应。结果表明，由于肌腱弹性的分段激活，肌腱运动的逐渐锁定和导向阻抗的增加导致更高的刚度。进一步证明，导轨所构成的阻抗的有效定制可用于生成动态最佳条件。这在模态阻尼最大化的特定情况下进行了说明，假设导向阻抗源自粘性阻尼的形式。鉴于这些见解，本研究认识到轴向激活肌腱在减振应用中的潜在延伸。