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Fractional-order stochastic resonance-based rescaling-frequency scanning images for early multi-frequency fault detection of machines 基于分数阶随机共振的重标频扫描图像用于机器早期多频故障检测
IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-02-05 DOI: 10.1016/j.ymssp.2026.113944
Yanan Gai , Zijian Qiao , Yanglong Lu , Ronghua Zhu , Xin Zhang
In engineering applications, weak multi-frequency fault signals from mechanical equipment are often masked by strong background noise. Traditional stochastic resonance (SR) methods mainly focus on enhancing fault signals into sine-like ones, but they may lose or even destroy the multi-harmonic characteristics of fault signals. To this end, this paper would propose a rescaling-frequency scanning image method using fractional-order SR (FSR-RFSI), aiming to enhance and visualize weak multi-frequency useful signals. First, the proposed method develops a fractional-order SR system with memory properties, which is designed to detect weak multi-frequency signals in complex spectral environments. Moreover, a weighted zero-crossing signal-to-noise ratio (WZCSNR) is proposed as a performance evaluation metric, which effectively overcomes the limitation of the traditional signal-to-noise ratio (SNR) that focuses solely on frequency-domain energy while neglecting time-domain multi-harmonic components. Meanwhile, to improve parameter tuning efficiency, this paper establishes an analytical relationship map between the resonant frequency and system parameters, namely rescaling-frequency scanning image. Furthermore, a quantum genetic algorithm (QGA) is used to achieve adaptive optimization of key system parameters. Simulation analyses and experiments on early rolling bearing and gearbox faults show that the proposed method can effectively boost and detect weak multi-frequency fault signals. Additionally, comparative analysis with Maximum Correlated Kurtosis Deconvolution (MCKD), Fast Kurtogram (FK), and Feature Modal Decomposition (FMD) methods further validates the superiority of the proposed method.
在工程应用中,机械设备微弱的多频故障信号往往被强背景噪声所掩盖。传统的随机共振方法主要是将故障信号增强为类正弦信号,但可能会失去甚至破坏故障信号的多谐特性。为此,本文提出了一种基于分数阶SR (FSR-RFSI)的重标频扫描图像方法,旨在增强和显示微弱的多频有用信号。首先,该方法开发了一种具有记忆特性的分数阶SR系统,用于检测复杂频谱环境下的微弱多频信号。此外,提出了加权过零信噪比(WZCSNR)作为性能评价指标,有效克服了传统信噪比(SNR)仅关注频域能量而忽略时域多谐波分量的局限性。同时,为了提高参数调谐效率,本文建立了谐振频率与系统参数的解析关系图,即重标频扫描图像。此外,采用量子遗传算法(QGA)实现系统关键参数的自适应优化。对滚动轴承和齿轮箱早期故障的仿真分析和实验表明,该方法可以有效地增强和检测微弱的多频故障信号。此外,通过与最大相关峰度反卷积(MCKD)、快速峰度图(FK)和特征模态分解(FMD)方法的对比分析,进一步验证了该方法的优越性。
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引用次数: 0
Novel variable inerter damper with independently tunable inertance and damping 具有独立可调的惯性和阻尼的新型可变阻尼器
IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-02-05 DOI: 10.1016/j.ymssp.2026.113954
Jubin Lu , Shitang Ke , Jinghua Lin , Songye Zhu
Inerter dampers (IDs) exhibit unique performance in various vibration control problems in comparison with other passive dampers. Most existing IDs can only possess fixed inertance and damping coefficients once manufactured, limiting their practical applications and the realization of adaptive or semi-active control. In this paper, a novel variable inerter damper (VID) design with superior tuning capabilities for both inertance and damping coefficients is developed. Unlike existing VIDs, the new VID design enables continuous and separate tuning of inertance and damping coefficients, conforming to control optimization that often requires precise, continuous, and separate tuning of these two coefficients. Theoretical modeling and extensive laboratory experiments were conducted to verify the performance of the VID prototype under various working conditions. Experimental results confirmed a broad tuning range for both inertance and damping, which, to the best of the authors’ knowledge, presents a first ton-level prototype exhibiting such extensive adjustability. Moreover, the inertance and EM damping coefficients can be tuned independently through their respective adjustment mechanisms. The salient characteristics of the proposed VID will significantly improve the functionality and applicability of IDs.
与其他无源阻尼器相比,惯性阻尼器在各种振动控制问题中表现出独特的性能。大多数现有的pid一旦制造出来就只能具有固定的惯性和阻尼系数,这限制了它们的实际应用和自适应或半主动控制的实现。本文提出了一种具有良好的惯性系数和阻尼系数可调能力的可变阻尼器设计。与现有的VID不同,新的VID设计可以连续和单独调整惯性和阻尼系数,符合通常需要精确、连续和单独调整这两个系数的控制优化。进行了理论建模和大量的实验室实验,验证了VID原型在各种工况下的性能。实验结果证实了惯性和阻尼的广泛调谐范围,据作者所知,这是第一个具有如此广泛可调性的吨级原型。此外,惯性系数和电磁阻尼系数可以通过各自的调节机制独立调节。所提出VID的显著特征将显著改善id的功能和适用性。
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引用次数: 0
RDI-Pred: Risk-aware and dynamics-enhanced trajectory prediction with intention guidance in emergency scenarios RDI-Pred:紧急情况下带有意图指导的风险意识和动态增强轨迹预测
IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-02-05 DOI: 10.1016/j.ymssp.2026.113975
Penglong Li , Hongyan Guo , Yanran Liu , Qingyu Meng , Shuang Liang , Dongpu Cao , Hong Chen
Trajectory prediction in emergencies scenarios is crucial for autonomous driving. Yet vehicle motion signals in these situations are highly nonlinear and nonstationary, with complex temporal and dynamic dependencies. Because mainstream datasets mainly cover regular driving and omit emergencies, existing models can still achieve satisfactory performance under normal conditions even without explicitly modeling exteroceptive cues, kinematic signals, or semantic intentions. However, during highly nonstationary and dynamic processes such as sudden cut-in or emergency braking, these weakly dependent architectures reveal significant shortcomings in generalization and robustness. To address these challenges, this paper proposes RDI-Pred, a multi-source temporal prediction framework that integrates Risk–Dynamics–Intention synergy from the perspectives of time-series signal processing and dynamic system modeling. First, we build a risk-aware exteroceptive encoder that uses prior-enhanced risk attention for risk scoring. Furthermore, a tri-agent interaction micrograph is constructed among the ego vehicle(Ego), target vehicle(TV), and closest in-path vehicle (CIPV) to model localized spatiotemporal dependencies, thereby enabling early-stage perception of exteroceptive risks. Next, we design a multi-scale Dynamics encoder that captures motion dynamics at short, mid, and long horizons. A 1D-CNN with a sliding window extracts short-term transients, BiGRU (Bidirectional Gated Recurrent Unit) states describe mid-term behavior, and a BiLSTM (Bidirectional Long Short-Term Memory) with self-attention models long-term dependencies, yielding a robust dynamic prior for trajectory decoding. Finally, we add cut-in intention recognition auxiliary task to constrain and re-score multi-modal trajectory candidates in decoding, promoting intention-aligned trajectories and suppressing mismatched ones. On the large-scale ESP high-risk dataset, RDI-Pred surpasses MTR with +32.9% mAP, -44.0% minADE, -45.9% minFDE, and -46.6% MR, showing clear performance gains across all key metrics. The results confirm its accuracy and robustness under emergency high-risk conditions, offering a practical path toward zero-tolerance safety in autonomous driving. Our code will be made publicly available at https://github.com/penglo/RDI-Pred-Risk-Dynamics-Intention-Collaborative-Vehicle-Trajectory-Prediction-in-Emergency-Scenarios .
紧急情况下的轨迹预测对自动驾驶至关重要。然而,在这些情况下,车辆运动信号是高度非线性和非平稳的,具有复杂的时间和动态依赖关系。由于主流数据集主要涵盖常规驾驶,忽略了紧急情况,因此即使没有明确建模外感受线索、运动学信号或语义意图,现有模型在正常情况下仍然可以获得令人满意的性能。然而,在高度非平稳和动态的过程中,如突然切断或紧急制动,这些弱依赖的体系结构在泛化和鲁棒性方面存在显着缺陷。为了解决这些挑战,本文提出了RDI-Pred,这是一个从时间序列信号处理和动态系统建模的角度集成了风险-动态-意图协同作用的多源时间预测框架。首先,我们构建了一个风险感知的外感编码器,该编码器使用先前增强的风险注意进行风险评分。此外,构建了自我载体(ego)、目标载体(TV)和最近路径载体(CIPV)之间的三智能体相互作用显微图,以模拟局部时空依赖性,从而实现对外感风险的早期感知。接下来,我们设计了一个多尺度动态编码器,可以捕获短、中、长视界的运动动态。带有滑动窗口的1D-CNN提取短期瞬态,BiGRU(双向门控循环单元)状态描述中期行为,带有自注意的BiLSTM(双向长短期记忆)模型描述长期依赖,为轨迹解码提供了鲁棒的动态先验。最后,我们增加了切入式意图识别辅助任务来约束和重新评分解码中的多模态轨迹候选者,促进意图一致的轨迹,抑制不匹配的轨迹。在大规模ESP高风险数据集上,RDI-Pred以+32.9%的mAP、-44.0%的minADE、-45.9%的minFDE和-46.6%的MR优于MTR,在所有关键指标上都表现出明显的性能提升。结果证实了该方法在紧急高风险条件下的准确性和鲁棒性,为实现自动驾驶零容忍安全提供了切实可行的途径。我们的代码将在https://github.com/penglo/RDI-Pred-Risk-Dynamics-Intention-Collaborative-Vehicle-Trajectory-Prediction-in-Emergency-Scenarios上公开提供。
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引用次数: 0
Decoupled multimodal vibration control of smart thin plates based on integrated observer 基于集成观测器的智能薄板解耦多模态振动控制
IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-02-05 DOI: 10.1016/j.ymssp.2026.113980
Xinyu Wen , Ang Song , Shengquan Li , Jia Guo
To address modal coupling and multi-source uncertainty in the multimodal vibration control of piezoelectric smart thin plates, this paper proposes an active vibration control strategy based on an integrated observer. First, an error-decoupling observer is designed to separate different vibration modes based on their frequency characteristics, achieving modal decoupling. Then, an independent cascaded backward recursive observer is employed to estimate the time-delay vibration signals of the decoupled modes with high precision. To compensate for sensor-induced phase delays and reduce input uncertainties, the estimated vibration signals are processed through predictive reconstruction, which enhances control accuracy and dynamic performance. The stability of the closed-loop system is guaranteed via Lyapunov analysis. Experimental results demonstrate that, compared with linear active disturbance rejection control with an extended state observer (LADRC-ESO), the proposed method achieves an additional attenuation of approximately 10 dB in vibration amplitude and an overall improvement of about 8% in vibration suppression. These results confirm the effectiveness of the proposed method.
针对智能压电薄板多模态振动控制中的模态耦合和多源不确定性问题,提出了一种基于集成观测器的主动振动控制策略。首先,设计误差解耦观测器,根据频率特性分离不同的振动模态,实现模态解耦;然后,采用独立的级联后向递归观测器对解耦模态的时滞振动信号进行高精度估计。为了补偿传感器引起的相位延迟和减少输入的不确定性,对估计的振动信号进行预测重构,提高了控制精度和动态性能。通过李雅普诺夫分析,保证了闭环系统的稳定性。实验结果表明,与带扩展状态观测器的线性自抗扰控制(LADRC-ESO)相比,该方法的振动幅度额外衰减约10 dB,总体振动抑制效果提高约8%。这些结果证实了所提方法的有效性。
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引用次数: 0
Dynamic response and sliding mode control of a cold rolling mill subjected to harmonic and Gaussian colored noise excitations 冷轧机在谐波和高斯有色噪声激励下的动态响应与滑模控制
IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-02-04 DOI: 10.1016/j.ymssp.2026.113971
Xiaofei Chen , Wei Zhang , Yufei Zhang
During operation, cold rolling mills are susceptible to the coupled effects of random excitations and structural nonlinearities, which can induce complex dynamic behaviors that adversely affect rolling quality and equipment safety. This paper studies the structural dynamic characteristics and vibration suppression for a two-degree-of-freedom cold rolling mill vertical structure model under combined harmonic and random excitation for the first time. Firstly, an averaging method and a stochastic method are extended to derive the amplitude-frequency and steady-state response equations, respectively. Secondly, the response shows the mill exhibits nonlinear hard spring characteristics and bistability in the resonance region. The coexistence and evolution of low- and high-amplitude attractors are further elucidated via the equivalent potential energy diagram and basin of attraction. Additionally, random excitation is a key factor inducing chaotic behavior in the rolling mill. Finally, Gaussian colored noise induces stochastic switching, stochastic P- and D-bifurcations. This can lead to defects in the rolled products, and in severe cases, it may even threaten the safe operation of the rolling mill. To suppress this catastrophic switching, this paper innovatively introduces the improved double power exponential reaching law to design sliding mode control, achieving faster convergence, suppressing chattering and reducing energy consumption. The proposed control has been rigorously proven to be stable and has been effectively verified through numerical simulations. The research findings provide essential theoretical foundations and technical support for the safe design and manufacture of vertical structural models for cold rolling mills in engineering practice.
冷轧机在运行过程中容易受到随机激励和结构非线性的耦合影响,产生复杂的动力行为,对轧制质量和设备安全产生不利影响。本文首次研究了二自由度冷轧机垂直结构模型在谐波和随机联合激励下的结构动力特性和振动抑制问题。首先,推广了平均法和随机法,分别推导了幅频响应方程和稳态响应方程。其次,在共振区,磨机具有非线性硬弹簧特性和双稳性。通过等效势能图和引力盆地进一步阐明了高低幅吸引子的共存和演化。此外,随机激励是引起轧机混沌行为的关键因素。最后,高斯色噪声诱导随机切换、随机P分岔和d分岔。这会导致轧制产品出现缺陷,严重时甚至会威胁到轧机的安全运行。为了抑制这种突变开关,本文创新性地引入改进的双功率指数趋近律来设计滑模控制,实现了更快的收敛、抑制抖振和降低能耗。通过数值仿真验证了所提出的控制方法是稳定的。研究结果为工程实践中冷轧机立式结构模型的安全设计与制造提供了必要的理论依据和技术支持。
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引用次数: 0
A Real-Time inverse method for moving contact force identification considering structural characteristics of Pantograph–Catenary system 考虑受电弓接触网结构特性的运动接触力实时反演识别方法
IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-02-04 DOI: 10.1016/j.ymssp.2026.113972
Haifei Wei, Ning Zhou, Xingshuai Zhi, Yao Cheng, Hongming Chen, Weihua Zhang
High-accuracy identification of contact force has long been a critical topic in the state monitoring of pantograph–catenary systems (PCS). This force contains key information for assessing current collection quality and diagnosing faults in both the pantograph and the catenary. With increasing train speeds and the emergence of more complex service conditions, traditional contact force measurements—typically limited to frequencies below 20 Hz—are no longer adequate. To address this limitation, this paper proposes a novel method for real-time contact force identification based on an inverse problem framework. First, a generalized elastically supported beam model is developed to describe the pantograph contact strip, allowing for accurate reconstruction of boundary conditions and load–response relationships. Second, a sliding window strategy is integrated with a sparse regularization technique, incorporating load dictionary matching and static force constraints, to enable online inversion of moving contact forces with high robustness and low latency. Based on the data of PCS simulation, the proposed method was validated to be effective and robust in identifying the contact force with complex characteristics. Furthermore, lab tests verified its effectiveness and feasibility for engineering applications. In addition, the discussion results indicate that the proposed approach exhibits low dependence on measurement point locations, strong capability in identifying impact loads, and good real-time performance. The approach offers a new and effective solution for wide frequency domain contact force identification in high-speed and variable operating environments.
接触力的高精度识别一直是受电弓接触网系统状态监测中的一个关键问题。该力包含评估电流收集质量和诊断受电弓和接触网故障的关键信息。随着列车速度的提高和更复杂的服务条件的出现,传统的接触力测量-通常限于低于20hz的频率-不再适用。为了解决这一问题,本文提出了一种基于逆问题框架的实时接触力识别方法。首先,建立了一个广义的弹性支承梁模型来描述受电弓接触带,从而可以精确地重建边界条件和载荷-响应关系。其次,将滑动窗口策略与稀疏正则化技术相结合,结合负载字典匹配和静力约束,实现了高鲁棒性和低延迟的运动接触力在线反演。基于PCS仿真数据,验证了该方法在识别具有复杂特性的接触力方面的有效性和鲁棒性。实验验证了该方法的有效性和工程应用的可行性。此外,讨论结果表明,该方法对测点位置的依赖程度低,对冲击载荷的识别能力强,实时性好。该方法为高速多变工作环境下的宽频域接触力识别提供了一种新的有效解决方案。
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引用次数: 0
Super-sensitivity full-field displacement measurement method based on convolutional variational autoencoder 基于卷积变分自编码器的超灵敏度全场位移测量方法
IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-02-04 DOI: 10.1016/j.ymssp.2026.113941
Shunxin Xia , Yuequan Bao , Feiyuan Long
Computer vision technology is an important means of non-contact displacement measurement, but its displacement measurement sensitivity is often limited by the rounding error of the camera during image acquisition. This error causes the image to retain only integer-bit pixel intensity values, making it difficult to characterize tiny displacements below the theoretical sensitivity limit. To address this problem, we propose a super-sensitive full-field displacement measurement method based on Convolutional Variational Autoencoder (CVAE). This method constructs a CVAE network model, introduces the standard deviation matrix as prior information, and designs a weighted reconstruction loss function to achieve accurate reconstruction of the decimal pixel intensity in the raw image data. The reconstructed image is processed in combination with the optical flow method to achieve super-sensitive full-field displacement measurement. The effectiveness of this method in super-sensitive displacement measurement is verified by numerical simulation and laboratory experiments, and it shows good robustness under partial occlusion and illumination changes. This method initially provides a feasible solution for high-precision full-field displacement measurement in complex scenes.
计算机视觉技术是非接触式位移测量的重要手段,但其位移测量灵敏度往往受到图像采集过程中摄像机舍入误差的限制。这个错误导致图像只保留整数位像素强度值,使其难以表征低于理论灵敏度限制的微小位移。为了解决这一问题,我们提出了一种基于卷积变分自编码器(CVAE)的超灵敏全场位移测量方法。该方法构建CVAE网络模型,引入标准差矩阵作为先验信息,设计加权重建损失函数,实现原始图像数据中十进制像素强度的精确重建。结合光流法对重构图像进行处理,实现了超灵敏的全场位移测量。数值模拟和室内实验验证了该方法在超灵敏位移测量中的有效性,在局部遮挡和光照变化情况下具有良好的鲁棒性。该方法初步为复杂场景下的高精度全场位移测量提供了可行的解决方案。
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引用次数: 0
Structured identification of multivariable modal systems 多变量模态系统的结构化辨识
IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-02-04 DOI: 10.1016/j.ymssp.2026.113948
M. van der Hulst , R.A. González , K. Classens , P. Tacx , N. Dirkx , J. van de Wijdeven , T. Oomen
Physically interpretable models are essential for next-generation industrial systems, as these representations enable effective control, support design validation, and provide a foundation for monitoring strategies. The aim of this paper is to develop a system identification framework for estimating modal models of complex multivariable mechanical systems from frequency response data. To achieve this, a two-step structured identification algorithm is presented, where an additive model is first estimated using a refined instrumental variable method and subsequently projected onto a modal form. The developed identification method provides accurate, physically-relevant, minimal-order models, for both generally-damped and proportionally damped modal systems. The effectiveness of the proposed method is demonstrated through experimental validation on a prototype wafer-stage system, which features a large number of spatially distributed actuators and sensors and exhibits complex flexible dynamics.
物理可解释的模型对于下一代工业系统至关重要,因为这些表示可以实现有效的控制,支持设计验证,并为监控策略提供基础。本文的目的是开发一个系统识别框架,用于从频率响应数据估计复杂多变量机械系统的模态模型。为了实现这一点,提出了一种两步结构化识别算法,其中首先使用改进的工具变量方法估计加性模型,然后将其投影到模态形式上。所开发的识别方法为一般阻尼和比例阻尼模态系统提供了准确的、物理相关的最小阶模型。通过实验验证了该方法的有效性,该系统具有大量空间分布的致动器和传感器,具有复杂的柔性动力学特性。
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引用次数: 0
A novel isolator with movable cyclic quasi-zero-stiffness enabling low-frequency vibration suppression under arbitrary loads 一种新型可动循环准零刚度隔振器,能在任意载荷下抑制低频振动
IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-02-04 DOI: 10.1016/j.ymssp.2026.113924
Yanfeng Liu , Haifeng Ou , Lingling Hu
Low-frequency vibration isolation capable of accommodating uncertain loads is in great demand in engineering applications. Active control is the dominant approach; however, it relies on complex computation, feedback, and compensation processes, leading to high resource consumption. Passive isolators are favored for their reliability, low cost, and structural simplicity. However, existing passive isolators generally perform well only under specific loads, whereas their isolation performance deteriorates significantly or even fails under other loads. This study proposes a novel passive isolator that enables low-frequency vibration suppression under arbitrary loads. It features cyclic quasi-zero-stiffness (QZS) characteristics, and the QZS plateaus can shift with the applied load to accommodate load variations. A theoretical model is developed to derive the conditions for achieving QZS, providing essential guidance for the design and adjustment of the isolator to continuously vary the QZS plateaus across the full bearing range, thus ensuring adaptive stiffness tuning under arbitrary loads. A prototype was fabricated and tested to validate its performance. Experiments confirm that, by simply adjusting the support height, the isolator can provide effective vibration isolation above 3.7 Hz under arbitrary loads across its entire load-bearing range (0–6500 g). The adjustment method is easy to implement and tolerant of low-precision operation. These results demonstrate that the proposed isolator offers a load-adaptive and robust solution for low-frequency vibration isolation, highlighting its strong potential for engineering applications.
能够适应不确定载荷的低频隔振在工程应用中有很大的需求。主动控制是主导方法;然而,它依赖于复杂的计算、反馈和补偿过程,导致较高的资源消耗。无源隔离器因其可靠性、低成本和结构简单而受到青睐。然而,现有的被动隔离器一般只在特定负载下表现良好,而在其他负载下其隔离性能会显著下降甚至失效。本研究提出一种新型无源隔振器,能在任意载荷下抑制低频振动。它具有循环准零刚度(QZS)特性,并且QZS平台可以随着外加载荷的变化而变化,以适应载荷的变化。建立了一个理论模型,推导了实现QZS的条件,为隔离器的设计和调整提供了必要的指导,以在整个轴承范围内连续改变QZS平台,从而确保在任意载荷下的自适应刚度调谐。制作了样机并对其性能进行了测试。实验证实,通过简单地调整支撑高度,隔振器可以在整个承重范围内(0-6500 g)的任意载荷下提供3.7 Hz以上的有效隔振。该调整方法易于实现,可承受低精度操作。结果表明,所提出的隔振器提供了一种负载自适应和鲁棒的低频隔振解决方案,突出了其强大的工程应用潜力。
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引用次数: 0
Design and analysis of a novel negative stiffness mechanism using cosine semi-circular beam for low frequency vibration isolation 余弦半圆梁低频隔振负刚度机构的设计与分析
IF 8.9 1区 工程技术 Q1 ENGINEERING, MECHANICAL Pub Date : 2026-02-04 DOI: 10.1016/j.ymssp.2026.113976
Pyla Prasad , Srajan Dalela , Akhand Rai , P.S. Balaji
This research article presents a Cosine Semi-Circular Beam (CSCB) inspired by the semi-circular arch with a cosine profile in lateral direction. The study investigates nonlinear stiffness of the CSCB to achieve low-frequency isolation. The isolator comprises two CSCBs coupled with four Semi-Circular Arch (SCA) elements to achieve the quasi-zero stiffness (QZS) property, which is crucial for vibration attenuation at low frequencies. The design of CSCB isolator is performed using finite element analysis and experimental procedures. Moreover, Symbolic Regression in julia programming language is employed to obtain the explicit equation for restoring force of the isolator. Static characteristics demonstrate the existence of QZS region in the force–displacement curve. Dynamic analysis is conducted by solving the equation of motion of the isolator using the Harmonic Balance Method (HBM) and the fourth order Runge–Kutta method (RK4). The dynamic response is scrutinised further for its chaotic behaviour using the displacement bifurcation diagram and the Lyapunov exponent across a range of excitation acceleration. Phase portraits at different frequencies illustrate the nonlinear response of the isolator changing from periodic to chaotic. The performance of the CSCB isolator at low frequencies is assessed through acceleration transmissibility, numerically, analytically and experimentally. Experimental findings from dynamic vibration test confirm the occurrence of sudden jump-down into the isolation region at 8Hz, while excitations above 9Hz can be effectively isolated.
本文提出了一种受横向余弦轮廓的半圆拱的启发而设计的余弦半圆梁。研究了CSCB实现低频隔离的非线性刚度。该隔振器由两个cscb和四个半圆弧(SCA)单元组成,以实现准零刚度(QZS)特性,这对低频振动衰减至关重要。采用有限元分析和实验方法对CSCB隔振器进行了设计。此外,采用julia编程语言中的符号回归,得到了隔振器恢复力的显式方程。静力特性表明在力-位移曲线中存在QZS区域。采用谐波平衡法(HBM)和四阶龙格-库塔法(RK4)求解隔振器的运动方程,进行了动力学分析。利用位移分岔图和李雅普诺夫指数在激励加速度范围内进一步检查动态响应的混沌行为。不同频率下的相位图说明了隔离器从周期到混沌的非线性响应。通过加速度传递率、数值、解析和实验对CSCB隔离器的低频性能进行了评价。动态振动试验结果证实,在8Hz时出现突然跳降进入隔离区,而在9Hz以上的激励可以有效隔离。
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Mechanical Systems and Signal Processing
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