具有可调屈曲行为的蛇形条带中的双特征值分岔与多稳态
Double-eigenvalue bifurcation and multistability in serpentine strips with tunable buckling behaviors
AI总结：
本文利用各向异性杆理论和连续延拓方法研究蛇形条带的屈曲行为，揭示双特征值分岔导致模态互换并改变稳定性，同时通过调控厚度和高度实现屈曲模态的可调设计，为柔性结构和多稳态器件提供指导。
摘要：
蛇形结构由直线段和圆弧段组成，因其出色的可拉伸性而作为柔性电子器件的潜在设计受到广泛关注。当受到拉伸时，这些蛇形条带会发生面外屈曲，此前的研究已经识别出两种不同的屈曲模态，并且在单胞蛇形结构中这两种模态的出现顺序可能发生互换。在本研究中，我们采用各向异性杆理论将蛇形条带建模为一个多段边值问题（BVP），并在直线段与弯曲段之间的界面处施加连续性条件。我们使用连续延拓方法求解该边值问题，结果表明：1）单胞蛇形条带中两种屈曲模态的互换是由一个双特征值及相关的二次分岔引起的，这些二次分岔同时改变了两种屈曲模态的稳定性；2）在桌面模型中可以通过手动方式获得多种具有可逆对称性的稳定状态，并且在数值连续延拓中发现这些状态与平面分支不相连。此外，我们证明，通过在不同胞元之间调节条带厚度，可以使屈曲在最薄截面处首先发生，从而实现对蛇形条带屈曲模态的调控。在具有两个胞元的结构中，通过设计具有非均匀高度的蛇形条带，也可以控制两种屈曲模态的出现顺序。这项工作可以提升基于蛇形互连的柔性结构的机械设计水平，并可能在多稳态致动器和机械存储器件中得到应用。
英文摘要：
Serpentine structures, composed of straight and circular strips, have garnered significant attention as potential designs for flexible electronics due to their remarkable stretchability. When subjected to stretching, these serpentine strips buckle out of plane, and previous studies have identified two distinct buckling modes whose order of appearance may interchange in serpentine structures with a single cell. In this study, we employ anisotropic rod theory to model serpentine strips as a multi-segment boundary value problem (BVP), with continuity conditions enforced at the interface between the straight and curved strips. We solve the BVP using methods of continuation, and our results reveal that: 1) the exchange of the two buckling modes in a single-cell serpentine strip is induced by a double-eigenvalue and associated secondary bifurcations, which also alter the stability of the two buckling modes; 2) a variety of stable states with reversible symmetry can be manually obtained in tabletop models and are found to be disconnected from the planar branch in numerical continuation. Furthermore, we demonstrate that modulating the strip thickness across different cells leads to the initiation of buckling in the thinnest section, thereby allowing for the tuning of buckling modes in serpentine strips. In structures with two cells, the sequence of the two buckling modes can also be controlled by designing serpentine strips with nonuniform height. This work could enhance the mechanical design of serpentine-interconnect-based flexible structures and could have applications in multistable actuators and mechanical memory devices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
