A limit point behaviour of a metastructure, composed of two double clamped, initially curved beams, coupled via a rigid truss at their respective centres, is studied when subjected to a distributed electrostatic load. The analysis is based on a reduced order (RO) model, resulting from Galerkin’s decomposition, with symmetric buckling modes used as the base functions. To better understand the behaviour of the structure, the electrostatic analysis is preceded by a study of the model under “mechanical”, displacement-independent, load, allowing validation against a finite elements (FE) model, which served as proving ground for the RO model. In addition, results obtained by the RO model are compared with those extracted via finite differences (FD) solutions, facilitating the usage of the latter as the reference in the electrostatic, displacement-dependent, analysis. To accommodate for winding equilibrium paths, all solutions employed the implicit arc-length “Riks” method. The analysis has produced complicated equilibrium paths, which necessitated a corresponding local stability analysis, conducted using the energy method, allowing for limit point characterisation. The analyses have shown that the double beam metastructure is able to possess bistable and tristable properties, usually found in highly complex structures, which can be cumbersome for design and miniaturisation, provided that it meets certain geometrical parameters. Several variations of tristability are disclosed in the study, hitherto unknown, providing insight to the complexity of the structure. The analysis indicates that a model with at least three degrees-of-freedom (DOF) is needed to predict the various critical thresholds with reasonable errors. In so doing, the model can be used for static characterisation and design of various applications, where a simple structure, possessing tristable properties, is required.

当受到分布式静电负载时，研究了由两个双夹紧、最初弯曲的梁组成的超结构的极限点行为，这些梁通过各自中心的刚性桁架耦合。该分析基于降阶 (RO) 模型，该模型由 Galerkin 分解产生，对称屈曲模式用作基本函数。为了更好地理解结构的行为，静电分析之前是在“机械”、与位移无关的载荷下研究模型，允许对有限元 (FE) 模型进行验证，该模型用作 RO 的试验场模型。此外，将 RO 模型获得的结果与通过有限差分 (FD) 解提取的结果进行比较，便于将后者用作静电中的参考，位移相关，分析。为了适应绕组平衡路径，所有解决方案都采用隐式弧长“Riks”方法。分析产生了复杂的平衡路径，需要相应的局部稳定性分析，使用能量方法进行，允许极限点表征。分析表明，双梁超结构能够具有双稳态和三稳态特性，通常在高度复杂的结构中发现，只要满足某些几何参数，这对于设计和小型化来说可能很麻烦。研究中揭示了迄今为止未知的三稳态变化，提供了对结构复杂性的深入了解。分析表明，需要一个至少具有三个自由度 (DOF) 的模型来预测具有合理误差的各种临界阈值。这样做时，该模型可用于需要具有三稳态特性的简单结构的各种应用的静态表征和设计。