International Journal of Non-Linear Mechanics最新文献

英文中文

Aerodynamic optimization design of a Z-shaped folding wing based on bionic leading-edge tubercle structure 基于仿生前缘结节结构的z型折叠机翼气动优化设计

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-12-01 Epub Date: 2025-08-27 DOI: 10.1016/j.ijnonlinmec.2025.105251

Jie Xu, YongChang Huang, XiangYing Guo

To enhance the aerodynamic performance of folding wings, this study investigates the effects of leading-edge tubercles on the aerodynamic characteristics of folded wings under high Reynolds number conditions and analyzes the optimization of aerodynamic performance by varying tubercle parameters. Numerical simulations are employed to evaluate both steady and unsteady aerodynamic behaviors of post-fold wing configurations. First, a steady-state aerodynamic analysis is conducted comparing tubercled leading-edge wings with baseline wings. Results indicate that the A06R26 tubercled wing exhibits a higher lift coefficient than the baseline wing under steady-state conditions, though all tubercled variants incur increased drag penalties. Additionally, it is demonstrated that increasing the tubercle wavelength can significantly enhance aerodynamic performance. The tubercles induce streamwise vortices at the leading edge, disrupting the originally continuous shock waves and altering the pressure distribution on the upper wing surface, which manifest as segmented low-pressure zones with wavelike patterns. This modification will delay flow separation and improve stall characteristics at high angles of attack. In terms of unsteady aerodynamics, the tubercled and baseline wings exhibit similar overall trends during dynamic folding. However, the tubercled wing demonstrate more pronounced unsteady effects at medium-to-low folding angles, suggesting that the tubercle structure influences the dynamic aerodynamic stability of the wing.

为了提高折叠翼的气动性能，研究了高雷诺数条件下前缘结核对折叠翼气动特性的影响，并分析了不同结核参数对折叠翼气动性能的优化。采用数值模拟方法对后折翼结构的定常和非定常气动特性进行了研究。首先，对结节型前缘翼和基线翼进行了稳态气动分析。结果表明，在稳态条件下，A06R26结核型机翼的升力系数高于基准机翼，尽管所有结核型机翼都会增加阻力。此外，还证明了增大结核波长可以显著提高气动性能。这些结节在前缘诱导出流向涡旋，破坏了原本连续的激波，改变了上翼表面的压力分布，表现为波纹状的分段低压区。这种改进将延缓气流分离并改善大迎角下的失速特性。在非定常空气动力学方面，结节翼和基线翼在动态折叠过程中表现出相似的总体趋势。然而，在中低折叠角度下，结节状机翼表现出更明显的非定常效应，这表明结节状结构影响了机翼的动态气动稳定性。

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引用次数: 0

Transient dynamics of a polynomial stiffness nonlinear vibration absorber: Theoretical and numerical investigations 多项式刚度非线性减振器的瞬态动力学：理论与数值研究

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-12-01 Epub Date: 2025-08-18 DOI: 10.1016/j.ijnonlinmec.2025.105242

Xiaoxin Dai , Xiaojun Wei , Lihua Tang

This paper presents thorough theoretical and numerical investigations of transient dynamics of a linear primary system coupled with a polynomial stiffness nonlinear vibration absorber (PNVA), recently proposed by some of the authors. The PNVA incorporates positive linear and cubic stiffnesses and negative quadratic stiffness, with properly chosen coefficients to ensure the nonlinear restoring force function has only one equilibrium point at the origin. Distinct dynamic behaviors of a PNVA, such as the potential presence of two folds in a slow invariant manifold (SIM) curve, are revealed, highlighting a clear contrast to the behavior of a traditional nonlinear energy sink (NES). A design approach for a PNVA is proposed such that its energy dissipation efficiency and robustness against both structural frequency and input energy variations are simultaneously optimized. Subsequently, a comprehensive performance comparison of PNVAs, cubic NESs, bistable NESs, and traditional tuned mass dampers under free decay vibration induced by initial conditions is conducted. It is concluded that the proposed PNVA exhibits the best robustness against structural frequency detuning and relatively good energy dissipation efficiency and robustness against input energy variation. The PNVA offers an effective solution to the challenge of robust vibration mitigation.

本文对一些作者最近提出的线性一次系统耦合多项式刚度非线性吸振器（PNVA）的瞬态动力学进行了深入的理论和数值研究。PNVA结合了正线性刚度和正三次刚度以及负二次刚度，通过适当选择系数来保证非线性恢复力函数在原点只有一个平衡点。揭示了PNVA的独特动态行为，例如在慢不变流形（SIM）曲线中可能存在两个折叠，突出了与传统非线性能量汇（NES）行为的明显对比。提出了一种同时优化PNVA的能量耗散效率和对结构频率和输入能量变化的鲁棒性的设计方法。随后，对PNVAs、三次NESs、双稳态NESs和传统调谐质量阻尼器在初始条件诱导的自由衰减振动下的性能进行了综合比较。结果表明，该方法对结构频率失谐具有较好的鲁棒性，对输入能量变化具有较好的能量耗散效率和鲁棒性。PNVA提供了一种有效的解决方案，以应对鲁棒减振的挑战。

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引用次数: 0

Free vibrations of an elastica around its post-buckled configurations 弹性材料绕其后屈曲结构的自由振动

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-12-01 Epub Date: 2025-09-01 DOI: 10.1016/j.ijnonlinmec.2025.105250

H. Kibach, A. Ture Savadkoohi, C.-H. Lamarque

The post-buckled free vibration problem of an elastica around one of its vibration modes is investigated. For this, different equilibrium states of the elastica are detected by analysing the dimensionless form of the governing equations. Then, the multiple scale method is employed to study the free vibration of the elastica in a selected post-buckled state around a specific vibration mode. At the micro-scale, the considered elastica can be supposed as an element of an architecture material with tailored mechanical behaviours.

研究了弹性结构绕某一振型的后屈曲自由振动问题。为此，通过分析控制方程的无量纲形式来检测弹性体的不同平衡状态。然后，采用多尺度法研究弹性材料在选定后屈曲状态下围绕特定振动模态的自由振动。在微观尺度上，弹性材料可以被认为是建筑材料的一个元素，具有定制的机械性能。

引用次数: 0

Features of different variants for optimal design of vibro-impact nonlinear energy sinks affecting their efficiency and dynamics 振动冲击非线性能量汇优化设计中不同变型的特性对其效率和动力学的影响

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-12-01 Epub Date: 2025-08-13 DOI: 10.1016/j.ijnonlinmec.2025.105220

Petro Lizunov , Olga Pogorelova , Tetyana Postnikova

This paper studies the performance of the vibro-impact nonlinear energy sinks (VI NESs) with different sets of optimized parameters under periodic excitation. Single-sided and double-sided VI NESs with different mass ratios are considered. Two variants of the damper parameter groups are presented, which exhibit sufficiently high but different efficiency for mitigating the primary structure (PS) vibrations. The high efficiency is maintained despite the complex damper dynamics with irregular movements and narrow areas of nonlinearity. The VI NESs with the smaller mass ratios show a special behavior. Some of their optimized parameters take on non-standard low-realistic values, namely, the clearance becomes very large and the damping coefficient becomes too small. The symmetry of the dynamics of a symmetric double-sided VI NES with a small mass ratio is broken. The dynamics becomes complex, with irregular motions and asymmetric impacts on the obstacles.

本文研究了周期激励下不同优化参数组的振动冲击非线性能量汇的性能。考虑了不同质量比的单面和双面VI度。提出了阻尼器参数组的两种变体，它们在抑制主结构振动方面表现出足够高但不同的效率。尽管阻尼器动力学复杂，运动不规则，非线性区域狭窄，但仍能保持高效率。质量比较小的VI表现出特殊的行为。他们的一些优化参数呈现出非标准的低真实感值，即间隙变得非常大，阻尼系数变得太小。破坏了小质量比对称双面VI NES的动力学对称性。动力学变得复杂，运动不规则，对障碍物的影响不对称。

引用次数: 0

Modal interactions between a linear oscillator and a nonlinear absorber: multiscale energy transfers 线性振荡器和非线性吸收器之间的模态相互作用：多尺度能量传递

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-12-01 Epub Date: 2025-08-19 DOI: 10.1016/j.ijnonlinmec.2025.105244

Lan Huang, Shufeng Lu, Wensai Ma

In aerospace engineering, considerable attention has been given to the use of a nonlinear energy sink (NES) as an efficient passive control device. This paper uses the Complexification-Averaging/Geometric Singular Perturbation Theory (CX-A/GSPT) to investigate the multiscale energy transfers in a forced two-DOF system coupled to a grounded NES (GNES) with both nonlinear grounded stiffness and damping. Due to the coexistence of fundamental resonance and internal resonance in the system, complex modal interactions occur between the linear oscillator (LO) and the GNES. In addition, the ratio of the mass of the GNES and the LO can be seen as a perturbation. This may lead to the occurrence of multiscale dynamics and energy transfers in the system. By using the CX-A method, the slow flow equations of the system can be obtained. Further application of GSPT can obtain the critical manifold that is equivalent to the so-called slow invariant manifold (SIM). With different values of nonlinear grounded stiffness and damping, the critical manifolds have different structures. These critical manifolds can capture diverse types of system responses. Moreover, Hilbert-Huang transform (HHT) is used to analyze the time-frequency-energy relationship of the system response. With different parameters, the instantaneous frequencies of the responses of the LO and GNES show a completely different change. The Hilbert spectra confirm the occurrence of complex modal interactions and different time-scale energy transfers in the system.

在航空航天工程中，非线性能量阱作为一种高效的被动控制装置受到了广泛的关注。本文采用复化平均/几何奇异摄动理论（CX-A/GSPT）研究了具有非线性接地刚度和阻尼的双自由度系统的多尺度能量传递问题。由于系统中存在基共振和内共振，线性振荡器（LO）与GNES之间存在复杂的模态相互作用。此外，GNES和LO的质量之比可以看作是一种扰动。这可能导致系统中出现多尺度动力学和能量转移。利用CX-A方法，可以得到系统的慢流方程。进一步应用GSPT可以得到等效于所谓慢不变流形（SIM）的临界流形。在不同的非线性接地刚度和阻尼值下，临界流形具有不同的结构。这些关键流形可以捕获不同类型的系统响应。利用Hilbert-Huang变换（HHT）分析了系统响应的时频能量关系。在不同的参数下，LO和GNES响应的瞬时频率表现出完全不同的变化。希尔伯特谱证实了系统中存在复杂模态相互作用和不同时标能量传递。

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引用次数: 0

Static bifurcations of short FPU softening chains with second-order interaction: The non-degenerate case 具有二阶相互作用的短FPU软化链的静态分岔：非简并情况

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-12-01 Epub Date: 2025-08-25 DOI: 10.1016/j.ijnonlinmec.2025.105246

Angelo Luongo , Manuel Ferretti , Noël Challamel

Fermi–Pasta–Ulam chains, made of

n = 2, 3, 4

masses, taut by an end force, are considered in the static field. Each mass has a second-order interaction with the surrounding masses. Springs are of cubic type, with softening behavior. The equilibrium equations are derived by the total potential energy theorem. The fundamental nonlinear path of each chain, exhibiting a limit point, is evaluated. Then, by controlling the loading process by a displacement, instead of the force, a bifurcation analysis is carried out, to investigate both the ascending and descending branches of the fundamental path. The analysis allows evaluating the exact bifurcation points along this path, which manifest in number of

n - 1

. The study also highlights the existence of a degenerate case in which all the bifurcation points coalesce at the limit point, an occurrence which is excluded here by assuming that all the bifurcation points are well-separated. The

n - 1

primary bifurcated paths are parametrically described in asymptotic form. Then, a post-bifurcation analysis is carried out along each of them, aimed at discovering further bifurcation points. Stability of all the branches found (first bifurcated and secondary bifurcated branches) is characterized from application of Lagrange–Dirichlet theorem. We show, for the present discrete nonlinear elastic systems, that for some parameters of interest, the first bifurcated branch may be stable, even if it loses stability in a secondary bifurcation scenario. The complex bifurcation scenario is depicted by 3D and 2D bifurcation diagrams, and asymptotic results validated by numerical analyses.

在静态场中考虑由n=2,3,4个质量组成的Fermi-Pasta-Ulam链，由端力拉紧。每个质量与周围的质量都有二阶相互作用。弹簧为立方型，具有软化性能。平衡方程由总势能定理导出。计算了每条链的基本非线性路径，并给出了一个极限值。然后，通过位移而不是力来控制加载过程，进行分岔分析，研究基本路径的上升和下降分支。分析允许评估沿着这条路径的精确分岔点，其数量为n−1。该研究还强调了一种退化情况的存在，在这种情况下，所有的分岔点在极限点合并，这种情况在这里通过假设所有的分岔点都很好地分开来排除。n−1条主分叉路径以渐近形式参数化描述。然后，沿着每个分支进行分岔后分析，旨在发现进一步的分岔点。利用拉格朗日-狄利克雷定理，对所得到的所有分支（一分岔和二次分岔）的稳定性进行了刻画。我们证明，对于目前的离散非线性弹性系统，对于一些感兴趣的参数，即使它在二次分岔情况下失去稳定性，第一次分岔分支也可能是稳定的。用三维分岔图和二维分岔图描述了复杂分岔情况，并通过数值分析验证了结果的渐近性。

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引用次数: 0

Self-sustained chaos and chaotic diode phenomenon in non-reciprocal coupled Duffing oscillators 非互易耦合Duffing振荡器中的自持续混沌和混沌二极管现象

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-12-01 Epub Date: 2025-08-06 DOI: 10.1016/j.ijnonlinmec.2025.105235

Andi Lai, Yuhang Li, Kai Wu, Xiaoning Liu

Research on nonreciprocity offers new theoretical insights and methods for controlling dynamical systems, demonstrating significant potential in vibration and wave manipulation. So far, most studies have focused on the behavior of linear systems, such as the non-Hermitian skin effect, nonreciprocal waves, and exceptional points. Here, we explore the nonreciprocity in chaotic systems by introducing nonreciprocal coupling between Duffing oscillators. We show that the nonreciprocal coupled oscillators can extract energy through closed displacement cycles, thus are able to compensate damping loss and sustain their chaotic motion. Further, we observe that, by adjusting the coupling strength, the system exhibits a chaotic diode effect, where chaos occurs only under excitation in one direction, while remaining stable under excitation in the opposite direction. The findings reveal complex oscillatory behavior arising from the combination of nonreciprocity and nonlinearity and shed light on new routes for tuning the chaotic oscillations of dynamic systems.

非互易性的研究为控制动力系统提供了新的理论见解和方法，在振动和波动操纵方面显示出巨大的潜力。到目前为止，大多数研究都集中在线性系统的行为上，如非厄米集肤效应、非互易波和异常点。在这里，我们通过引入Duffing振子之间的非互易耦合来探讨混沌系统中的非互易性。我们证明了非互易耦合振子可以通过封闭的位移周期提取能量，从而能够补偿阻尼损失并维持其混沌运动。此外，我们观察到，通过调节耦合强度，系统表现出混沌二极管效应，其中混沌只在一个方向的激励下发生，而在相反方向的激励下保持稳定。研究结果揭示了由非互易和非线性相结合引起的复杂振荡行为，并为动态系统混沌振荡的调谐提供了新的途径。

引用次数: 0

Transient response and stochastic bifurcation of a Rijke tube model based on path integral method 基于路径积分法的Rijke管模型的瞬态响应和随机分岔

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-12-01 Epub Date: 2025-08-05 DOI: 10.1016/j.ijnonlinmec.2025.105212

Chen Jin , Jiankang Liu , Wei Xu

The noise-induced dynamics are of paramount importance in thermoacoustic systems due to the ubiquity of noise in various practical combustion systems. However, the intrinsic mechanisms of noise-induced dynamics are usually too complicated to conduct an exhaustive investigation. In this study, we conduct a detailed investigation on the transient response and stochastic bifurcation in a Rijke tube model based on the path integral method. This study suggest that the heater power and time delay can induce stochastic P-bifurcation, while noise intensity cannot induce stochastic P-bifurcation, and only has a slight quantitative effect on the stationary probability density function. All these findings will be beneficial to the theoretical research of noise-induced transitions and the practical guidance for the design of thermoacoustic devices in the presence of noise.

由于各种实际燃烧系统中噪声的普遍存在，噪声诱导动力学在热声系统中具有至关重要的意义。然而，噪声诱导动力学的内在机制通常过于复杂，无法进行详尽的研究。在本研究中，我们基于路径积分法对Rijke管模型的瞬态响应和随机分岔进行了详细的研究。本研究表明，加热器功率和时间延迟可以引起随机p分岔，而噪声强度不能引起随机p分岔，并且对平稳概率密度函数只有轻微的定量影响。这些研究结果对噪声诱导跃迁的理论研究和噪声存在下热声器件的设计具有实际指导意义。

引用次数: 0

Isolation performances of combined system with large amplitude nonlinearity and dynamic vibration absorber 大振幅非线性与动态吸振器组合系统的隔振性能

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-12-01 Epub Date: 2025-08-22 DOI: 10.1016/j.ijnonlinmec.2025.105243

Yuntian Zhang, Xiuting Sun, Jian Xu

The vibration isolation performance of a combined vibration isolation (CVI) system incorporating triple quasi-zero stiffness (TQZS) and a dynamic vibration absorber (DVA) is investigated in this paper. The influences of mass ratio and static characteristics on the CVI system are analyzed, and the superior isolation performances of the CVI system compared to both the basic TQZS system and the QZS-DVA system are validated. The coupled effects of enhanced vibration absorption and weakened achievable optimal static characteristics, resulting from increased mass ratio, on the CVI system’s isolation performance are explored. Significant advantages of the CVI system are observed, not only compared to traditional QZS-DVA systems, but also compared to high-order single QZS-DVA systems at larger excitation amplitudes. Greater robustness in the tuning frequency is demonstrated by the CVI system when compared to the QZS-DVA system, leading to effective adaptation across a wider range of excitation amplitudes and reducing the reliance on adaptive tuning. An upward shift of the Pareto frontiers is observed with increasing mass ratio, resulting in a degradation of the achievable static characteristics of the CVI system. Improved robustness can be maintained by ensuring a low restoring force at the zero-stiffness point located away from the equilibrium, when the TQZS characteristics are selected from the Pareto frontiers.

研究了三准零刚度（TQZS）和动态吸振器（DVA）组合隔振系统的隔振性能。分析了质量比和静态特性对CVI系统的影响，验证了CVI系统相对于基本TQZS系统和QZS-DVA系统具有优越的隔震性能。探讨了质量比增大导致的吸振增强和可达到的最优静态特性减弱对CVI系统隔振性能的耦合影响。CVI系统不仅与传统的QZS-DVA系统相比，而且与大激励幅值的高阶单QZS-DVA系统相比，都具有显著的优势。与QZS-DVA系统相比，CVI系统在调谐频率方面具有更强的鲁棒性，可以有效地适应更大范围的激励幅度，并减少对自适应调谐的依赖。随着质量比的增加，观察到帕累托边界向上移动，导致CVI系统可实现静态特性的退化。当从Pareto边界中选择TQZS特征时，可以通过确保在远离平衡的零刚度点处的低恢复力来保持改进的鲁棒性。

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引用次数: 0

A compactor-soil coupling model considering mechanical inertia and its delayed feedback active suspension control 考虑机械惯量的压实土耦合模型及其延迟反馈主动悬架控制

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-12-01 Epub Date: 2025-08-18 DOI: 10.1016/j.ijnonlinmec.2025.105245

Dong Feng

Compactors have been widely employed in civil engineering projects, including pavement construction, railway embankments, and dam foundations. To investigate compactor-soil interaction dynamics, researchers have developed numerous dynamic models to optimize compaction efficiency. Traditional modeling approaches typically neglected the mechanical inertia of compactor suspension systems for simplification purposes. However, this simplification underestimates the filtering effect of suspension mass on vibration excitation, resulting in compromised phase delay characterization and high-frequency dynamic response prediction. These limitations adversely affect both control strategy effectiveness and model prediction accuracy. To overcome these limitations, this study develops an innovative compactor-soil coupling model incorporating mechanical inertia to more accurately simulate compactor dynamics. The research systematically examines the dynamic differences introduced by inertia consideration. The results reveal that mechanical inertia significantly prolongs the transient response time. Specifically, the steady-state times of the frame increases from 8.03 s to 55.78 s, while the steady-state times of the drum rises from 4.57 s to 27.06 s. Consequently, delayed feedback active suspension control is implemented to effectively suppress system oscillations, reducing the steady-state times to 14.31 s (frame) and 7.67 s (drum) using a displacement gain equal to three times the frame stiffness. Comparative analyses demonstrate the superior adaptability of the proposed coupling model in characterizing compactor dynamic responses. This advanced model not only provides practical solutions for enhancing vibration isolation and compaction quality but also establishes a theoretical foundation for developing next-generation intelligent compaction systems.

压实机已广泛应用于土木工程项目，包括路面施工、铁路路堤和大坝基础。为了研究压实机与土壤的相互作用动力学，研究人员开发了许多动态模型来优化压实效率。传统的建模方法通常为了简化而忽略了压路机悬挂系统的机械惯性。然而，这种简化低估了悬架质量对振动激励的滤波作用，导致相位延迟表征和高频动态响应预测受到损害。这些限制对控制策略的有效性和模型预测精度都有不利影响。为了克服这些限制，本研究开发了一种创新的压实机-土壤耦合模型，该模型考虑了机械惯性，以更准确地模拟压实机的动力学。本研究系统地考察了惯性考虑所带来的动态差异。结果表明，机械惯量显著延长了瞬态响应时间。其中，车架的稳态时间从8.03 s增加到55.78 s，滚筒的稳态时间从4.57 s增加到27.06 s。因此，延迟反馈主动悬架控制实现有效抑制系统振荡，减少稳态时间为14.31秒（帧）和7.67秒（鼓）使用位移增益等于三倍的框架刚度。对比分析表明，所提出的耦合模型在描述压实机动态响应方面具有较好的适应性。这种先进的模型不仅为提高隔振和压实质量提供了实用的解决方案，而且为开发下一代智能压实系统奠定了理论基础。

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