多稳态串联折纸结构的非线性动力学特性

折纸结构和折纸力学超材料由于其无穷的设计空间、出色的变形能力、超常规力学特性和广泛的应用前景,最近受到了学术界和工程界的 广泛关注.特别地,某些折纸结构单胞由于具有独特的双稳态特性而获得深入研究.注意到折纸结构和折纸超材料通常由多胞构成,但多胞 结构的多稳态特性及其诱发的动力学行为尚不清晰,相关的研究还较少.本文在双稳态Miura-ori堆叠结构单胞的基础上,研究由两个异构 双稳态单胞基于力平衡串联而成的结构.静力学分析指出,双胞串联结构具有4个定性不同的稳定构型,呈现出多稳态特征.动力学分析指 出,双胞串联结构在4个稳定构型处具有显著不同的固有频率特征. 逐渐增大激励幅值,双胞串联结构的多稳态特性诱发出类型丰富的复杂 非线性动力学响应,包括亚谐、超谐甚至混沌的阱内和阱间振动. 根据幅值特征,我们将稳态动力学响应分为九类,并开展了动力学响应的 吸引盆和吸引盆稳定性分析.结果表明,不同类型动力学响应的吸引盆稳定性(即出现概率)显著不同,且与激励幅值密切相关.本文得到的 多稳态双胞串联结构的静力学特性、动力学响应的分类,以及吸引盆稳定性相对于激励幅值的演化规律,对深入认识多稳态折纸结构的非 线性动力学特性,调控非线性动力学响应具有参考价值和指导意义. 

NONLINEAR DYNAMICAL CHARACTERISTICS OF A MULTI-STABLE SERIES ORIGAMI STRUCTURE 1)

Recently, origami structures and origami mechanical metamaterials receive extensive attention from the science and engineering communities due to the infinite design space, excellent deformability, extraordinary mechanical properties, and wide application potentials. In particular, some origami structures have been well studied due to their unique bistability. Note that origami structures and origami metamaterials are always composed of multiple cells; however, for multi-cell origami structures, their multistability characteristics and the induced dynamical behaviors have not been well understood. On the basis of the bistable stacked Miura-ori structure, this paper studies an origami structure connected by two heterogeneous cells in series based on force balance. Static analysis suggests that the two-cell series structure have four different stable configurations, exhibiting a multi-stable profile. Dynamical analysis reveals that the two-cell series origami structure presents significantly different natural frequencies at the four stable configurations. With the increase of the excitation amplitude, the multistability of the two-cell series structure could induce complex nonlinear dynamical responses, including intrawell and interwell oscillations that are sub-harmonic, super-harmonic, or even chaotic. They can be classified into nine types based on the response amplitude characteristics. Moreover, the basin of attraction and the basin stability of these dynamical responses are examined. The results indicate that the basin stabilities (i.e., the appearing probabilities) of these types of dynamical response are significantly different and closely relate to the excitation amplitude. In summary, the outcomes of this paper, i.e., the static characteristics of the two-cell series structure, the classification on dynamical responses, and the evolution rule of the basin stabilities with respect to the excitation amplitude, would contribute to the understanding on the nonlinear dynamics of multi-stable origami structures, and provide the basis for controlling the nonlinear dynamical responses.