简并Duffing振子的极端刚度：上田忽略的一个特征

IF 2.3 4区工程技术 Q3 MECHANICS

Mechanics Research Communications Pub Date : 2025-08-21 DOI:10.1016/j.mechrescom.2025.104504

Sergey V. Kuznetsov

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引用次数: 0

摘要

上田发现了一个奇怪的吸引子，它出现在庞卡罗剖面中，与确定性混沌有关，对应于线性刚度消失的简并Duffing强迫谐振子。通过将运动方程简化为一个自治系统，构造相应的雅可比矩阵，并分析其特征值，发现该系统具有极强的刚度：当位移接近于零时，其刚度比趋于无穷大。这种极高的刚度比使得显式数值方法不适合积分运动方程，因为它们在这种条件下不稳定。因此，Ueda的原始分析（1985）基于使用显式单步龙格-库塔-吉尔四阶解算器（RK4）结合汉明窗口，可能被认为对于捕获系统的真实动力学是不可靠的。

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On the extreme stiffness of degenerate Duffing oscillator: A feature overlooked by Ueda

Ueda’s discovery of a strange attractor, which appears in the Poincaré section and is associated with deterministic chaos, corresponds to a degenerate Duffing forced harmonic oscillator with vanishing linear stiffness. By reducing the equation of motion to an autonomous system, constructing the corresponding Jacobian matrix, and analysing its eigenvalues, it was found that the system is extremely stiff: its stiffness ratio tends to infinity as the displacement approaches zero. This extremely high stiffness ratio renders explicit numerical methods unsuitable for integrating the equation of motion due to their instability under such conditions. Consequently, Ueda’s original analysis (1985)—based on the use of an explicit single step Runge–Kutta–Gill 4th-order solver (RK4) combined with a Hamming window—may be considered unreliable for capturing the true dynamics of the system.

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来源期刊

Mechanics Research Communications 物理-力学

CiteScore

4.10

自引率

4.20%

发文量

114

审稿时长

9 months

期刊介绍： Mechanics Research Communications publishes, as rapidly as possible, peer-reviewed manuscripts of high standards but restricted length. It aims to provide: • a fast means of communication • an exchange of ideas among workers in mechanics • an effective method of bringing new results quickly to the public • an informal vehicle for the discussion • of ideas that may still be in the formative stages The field of Mechanics will be understood to encompass the behavior of continua, fluids, solids, particles and their mixtures. Submissions must contain a strong, novel contribution to the field of mechanics, and ideally should be focused on current issues in the field involving theoretical, experimental and/or applied research, preferably within the broad expertise encompassed by the Board of Associate Editors. Deviations from these areas should be discussed in advance with the Editor-in-Chief.