Page 257 - 《振动工程学报》2026年第5期

第 39 卷第 5 期 振 动 工 程 学 报 Vol. 39 No. 5
2026 年 5 月 Journal of Vibration Engineering May 2026

双 稳 态 周 期 结 构 带 隙 调 制

刘恩彩， 张 瑞， 曾文波

（长沙学院电子信息与电气工程学院，湖南 长沙 410022）

摘要：双稳态结构因其独特的非线性特性，在低频隔振和能量俘获等领域展现出巨大的应用潜力。本文聚焦由双稳态屈曲梁
构成的周期结构，通过施加静态预压缩，实现一种无需重新设计结构的带隙调谐机制。建立了该双稳态周期结构的等效离散
模型，并通过准静态压缩试验标定了模型的关键非线性参数。基于能量景貌理论，揭示了施加静态预压缩量能够有效调制系
统等效刚度的内在机理。通过理论解析、数值仿真和振动试验，研究了预压缩量对一维双稳态周期结构带隙特性的影响规
律。研究结果表明：通过增大屈曲梁的预压缩量，可以连续、单调地降低系统的等效刚度，从而使带隙的起始频率向低频区偏
移。当系统趋近于临界“零刚度”状态时，带隙可被调谐至接近 0 Hz。振动试验验证了该调谐策略的有效性，结果显示，在小
强度与大强度激励下，带隙起始频率分别实现了 52 和 56 Hz 的迁移。本研究可为设计具有低频、宽带、可调隔振特性的力学
超材料提供依据。

关键词： 非线性动力学；双稳态结构；带隙调谐；能量景貌
中图分类号：O322 文献标志码：A DOI：10.16385/j.cnki.issn.1004-4523.202507073

Bandgap tuning in bistable periodic structures

LIU Encai，ZHANG Rui，ZENG Wenbo
（Department of Electronic Information and Electrical Engineering，Changsha University，Changsha 410022，China）

Abstract： The fixed operational frequency ranges of conventional mechanical metamaterials severely limit their adaptability in complex
environments. Bistable structures， leveraging their inherent nonlinear properties， provide a promising foundation for developing tunable
systems. This paper presents a robust mechanism for tuning the bandgap of a periodic structure composed of bistable buckled beams.
The proposed strategy，based on applying static pre-compression，offers a passive yet highly effective alternative to methods requiring active
materials or complete structural redesign. The investigation integrates theoretical modeling， numerical simulation， and experimental
validation. The complex continuum mechanics of the one-dimensional periodic structure were abstracted into an equivalent discrete spring-
mass-damper model. Its key nonlinear parameters —the negative linear stiffness and positive cubic stiffness coefficients —were precisely
calibrated via quasi-static compression experiments on a unit cell fabricated using additive manufacturing with thermoplastic polyurethane
(TPU). The energy landscape theory was employed to elucidate the intrinsic tuning mechanism. The results reveal that static pre-compression
asymmetrically alters the characteristic ‘W’-shaped potential energy profile，thereby modifying the curvature at the equilibrium position. This
modulation of the potential well’s geometry enables continuous control over the system’s local equivalent stiffness and can induce a topological
transition from a bistable to a monostable state. The findings reveal a strong correlation between the applied pre-compression and the bandgap
location. Increasing the pre-compression on the buckled beams results in a continuous and monotonic decrease in the system’s equivalent
stiffness. Consequently，the bandgap’s starting frequency shifts towards the lower frequency region，with theoretical predictions indicating a
tunable range from 207 Hz down to near-zero frequencies. As the system approaches a critical “zero-stiffness” state—where a potential well
coalesces with the energy barrier —the potential for ultra-low frequency isolation is unlocked. The efficacy of this tuning strategy was
experimentally validated using an 8-cell prototype，demonstrating significant shifts in the bandgap starting frequency of 54% and 64% under
small and large intensity excitations， respectively. The system exhibited characteristic softening nonlinearity， evidenced by a further
downward shift of the bandgap at higher excitation amplitudes. This research establishes a robust and accessible methodology for bandgap
manipulation， providing a foundational reference for the design of next-generation mechanical metamaterials with low-frequency，
broadband，and tunable vibro-acoustic properties.
Keywords：nonlinear dynamics；bistable structure；bandgap tuning；energy landscape

收稿日期：2025-07-31；修订日期：2025-11-04