发表机构
P. M. Rady Department of Mechanical Engineering, University of Colorado Boulder（科罗拉多大学博尔德分校 P.M. 雷迪机械工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过数学分析与数值模拟，证明离散屈曲环在横向简谐激励下，仅当基础非线性时可通过参数共振激活旋转软模态，并揭示三种动态响应行为，为软机器人驱动和纳米操控提供新途径。
AI 中文摘要
在本研究中，我们探讨了在横向简谐激励下，离散屈曲环中出现的旋转振动模态的存在性及其特征。该研究通过数学分析并结合数值模拟进行。环由均匀分布的集中质量组成，这些质量通过线性弹簧和扭转弹簧连接，并由弹性基础支撑。所关注的屈曲状态源于均匀的面内压缩，其特征是具有旋转性质的振动模态，这是由于系统的旋转对称性所致。由此产生的振动模态称为旋转软模态，其特点是环的变形具有大幅度的旋转，同时保持其角动量为零。研究表明，旋转软模态可以通过横向简谐激励经由参数共振被激活，而这只有在基础引入非线性时才可能实现。在缺乏非线性行为的情况下，环的横向振动不能导致旋转模态的激发。对约束运动学模型的分析表明，基础的线性刚度会导致旋转模态与横向振动解耦。当基础被视为分段线性，即在压缩和拉伸时具有不同的刚度值时，研究表明受迫环的动态响应可能出现三种不同的行为：i) 无旋转；ii) 在有限的旋转角度范围内出现极限环；iii) 在随后的平衡角度之间产生诱导旋转。本研究有助于理解屈曲结构中软模态的激活与控制，并可能为软机器人中的驱动应用以及纳米力学背景下分子系统的高级操控策略提供启示。
英文摘要
In the present study, we explore the existence and characteristics of a rotating vibrational mode in a discrete buckled ring that manifests under transverse harmonic forcing. The study is conducted through mathematical analysis complemented by numerical simulations. The ring is composed of uniformly distributed concentrated masses connected by linear and torsional springs and supported by an elastic foundation. The buckled state of interest results from homogeneous in-plane compression and is characterized by vibrational modes that have a rotating nature because of the rotational symmetry of the system. The resulting vibrational mode, called a rotational soft mode, is characterized by large amplitude rotations of the ring deformation while keeping its angular momentum zero. It is shown that rotational soft modes can be activated via transverse harmonic forcing through parametric resonance, which is possible only when nonlinearities are introduced to the foundation. In the absence of nonlinear behavior, transverse vibrations of the ring cannot lead to excitation of the rotational mode. Analysis of a constrained kinematics model shows that linear stiffness of the foundation leads to decoupling of the rotational mode from transverse vibrations. When the foundation is considered piecewise linear, with different stiffness values in compression and in extension, it is shown that three different behaviors are possible for the dynamic response of the forced ring: i) no rotation, ii) a limit cycle within a limited finite rotation angle range, iii) induced rotation between subsequent equilibrium angles. The present study contributes to the understanding of the activation and control of soft modes in buckled structures and may lead to actuation applications in soft robotics, as well as advanced manipulation strategies of molecular systems in the context of nanomechanics.
Journal refInternational Journal of Solids and Structures 341 (2026) 114332
DOI：10.1016/j.ijsolstr.2026.114332
