Non-reciprocity of energy transfer derived from cubic stiffness-induced nonlinear phenomena

IF 4.4 2区物理与天体物理 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Results in Physics Pub Date : 2025-05-04 DOI:10.1016/j.rinp.2025.108290

Na Kong , Min Sun , Jianen Chen

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Abstract

Introducing purely nonlinear elastic elements can induce rich dynamic behaviors, such as bifurcations, jumps and isolated resonance curves, to linear systems. Therefore, these elements are suitable for constructing strong non-reciprocity of vibration energy transfer. First, the energy transfer along reciprocal directions in a three-degree-of-freedom system is investigated, where three oscillators are connected by cubic springs. The semi-analytical solutions of the system are obtained using the complexification-averaging method and the least squares method. The results are compared against numerical solutions obtained by the Runge-Kutta method. The excitation amplitude range that produces strong non-reciprocity of vibration energy is analyzed. The jump phenomenon under combined excitation is investigated, and a trigger method for constructing non-reciprocity using an impulse is proposed. Then, an oscillator chain with cubic stiffness and scaling parameters is embedded into a multi-degree-of-freedom linear oscillator system to further explore the effect of cubic stiffness. Energy transfer along two directions is compared by exciting the leftmost oscillator and the rightmost oscillator. Moreover, the trigger effect of the impulse on non-reciprocity is demonstrated. The results show significant differences in vibration energy transfer within three distinct frequency bands. The critical points between reciprocal and non-reciprocal states are obtained, and the three stages of reciprocity related to excitation amplitude are analyzed. Lastly, the modulation effect of the cubic stiffness on non-reciprocity is conducted by comparing the energy of the output oscillator.

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由三次刚度非线性现象导出的能量传递的非互易性

引入纯非线性弹性单元可以引起线性系统丰富的动力学行为，如分岔、跳变和孤立共振曲线。因此，这些单元适用于构造振动能量传递的强非互易性。首先，研究了三自由度系统中三个振子由三次弹簧连接的能量沿反方向传递。利用复化平均法和最小二乘法得到了系统的半解析解。结果与龙格-库塔法的数值解进行了比较。分析了产生强非互易振动能量的激励幅值范围。研究了组合激励下的跳变现象，提出了一种利用脉冲构造非互易的触发方法。然后，将具有三次刚度和标度参数的振子链嵌入到多自由度线性振子系统中，进一步探讨三次刚度的影响。通过激发最左边的振子和最右边的振子，比较了沿两个方向的能量传递。此外，还证明了脉冲对非互易的触发效应。结果表明，在三个不同频带内，振动能量传递存在显著差异。得到了互易和非互易状态之间的临界点，分析了与激励幅值相关的互易的三个阶段。最后，通过比较输出振子的能量，分析了三次刚度对非互易的调制作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Results in Physics MATERIALS SCIENCE, MULTIDISCIPLINARYPHYSIC-PHYSICS, MULTIDISCIPLINARY

CiteScore

8.70

自引率

9.40%

发文量

754

审稿时长

50 days

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