可编程非线性刚度耦合的准零刚度超结构设计
DESIGN OF QUASI-ZERO STIFFNESS METASTRUCTURES WITH PROGRAMMABLE NONLINEAR STIFFNESS COUPLING
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摘要: 准零刚度结构具有高静低动的特点, 在静平衡位置附近低动刚度, 同时保持高静刚度, 解决了传统隔振技术在低频隔振时难以兼顾刚度和承载的困境. 目前关于准零刚度的研究主要集中在利用弹簧机构的大尺度独立结构实现高静低动特性, 针对微型仪器或需连续承载的仪器而言弹簧机构的微型化与安装难以实现. 为了克服这个问题本研究提出一种新型余弦梁准零刚度超结构, 该结构准零刚度特性源于双余弦梁突弹跳变行为产生的负刚度力学特性和镜像布置的双余弦梁弯曲主导的非线性正刚度力学特性耦合实现. 通过建立单胞结构的力学模型从理论上推导了该超结构的力学特性, 并利用数值仿真和试验验证了该理论模型的有效性, 结果表明: 平台力的试验结果与理论值相对误差为4.3%, 此外, 相较于线性正刚度的设计, 该结构平台力提高了25.6%, 充分证明了非线性正刚度的优势. 在此基础上进一步探讨对结构参数对力学性能的影响, 结合仿真和试验, 进一步研究阵列排布单胞的方式对准零刚度效应的调节机制. 通过仿真和试验进一步研究阵列排布单胞的方式对准零刚度效应的调节, 水平排布可增加承载能力, 垂直排布可拓宽准零刚度区间, 这种规律使整体结构具有可编程性. 本研究利用余弦梁结构非线性刚度耦合, 实现了高刚度宽准零刚度区间的静态力学性能, 对载荷定制化的准零刚度超结构的设计具有重要的指导意义.Abstract: Quasi-zero stiffness structures exhibit high static stiffness and low dynamic stiffness. They maintain high static stiffness while exhibiting low dynamic stiffness near the static equilibrium position, thereby resolving the challenge faced by traditional vibration isolation technologies in achieving both adequate stiffness and load-bearing capacity during low-frequency isolation.Current research on quasi-zero stiffness primarily focuses on achieving high static and low dynamic characteristics through large-scale independent spring mechanisms. However, miniaturizing and installing such spring mechanisms remains challenging for micro-instruments or instruments requiring continuous load-bearing.To overcome this issue, this study proposes a novel Cosine Beam Quasi-Zero Stiffness Metastructure (CBQM). Its quasi-zero stiffness property arises from the coupling of two distinct mechanical characteristics: negative stiffness resulting from the double cosine beam's sudden bounce behavior, and nonlinear positive stiffness dominated by the bending of the mirror-arranged double cosine beams.The mechanical properties of this metastructure were theoretically derived by establishing a mechanical model of its monolithic structure. The validity of this theoretical model was verified through numerical simulations and experimental validation. Results indicate that the experimental platform force deviated from theoretical values by only 4.3%. Furthermore, compared to designs with linear positive stiffness, this structure achieved a 25.6% increase in platform force, fully demonstrating the advantages of nonlinear positive stiffness.Building upon this foundation, we further investigate the influence of structural parameters on mechanical properties. By integrating simulation and experimental studies, we explore the regulatory mechanism of quasi-zero stiffness effects through the arrangement of array units. Simulation and testing reveal that horizontal unit arrangement enhances load-bearing capacity, while vertical arrangement broadens the quasi-zero stiffness range. This pattern endows the overall structure with programmability.This study utilizes the nonlinear stiffness coupling of a cosine beam structure to achieve high-stiffness static mechanical properties with a wide quasi-zero stiffness range, providing significant guidance for designing load-customized quasi-zero stiffness metastructures.
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