International Journal of Non-Linear Mechanics最新文献_第4页

Periodic and chaotic responses of flexible bistable energy harvesters in rotational environment 旋转环境下柔性双稳态能量采集器的周期和混沌响应

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-09-15 DOI: 10.1016/j.ijnonlinmec.2025.105264

Suo Wang , He Ma , Zhiyuan Li , Houfan Du , Shengxi Zhou

For the dual-beam coupled flexible bistable energy harvester (FBEH) with time-varying potential wells, accurately fitting the magnetic forces in two directions simultaneously using polynomials is difficult, hindering the derivation of the analytical solutions. Therefore, in this study, a semi-analytical method that combines the incremental harmonic balance method (IHBM) and the arc-length method is employed to determine the periodic solutions, with stability assessed by the Floquet theory. Comprehensive analyses of the dynamic responses are conducted, encompassing jump phenomenon, multiple solutions, and bifurcation characteristics. The obtained semi-analytical solutions demonstrate an excellent approximation for the system's periodic responses. Subsequently, the chaotic responses are analyzed via the Lyapunov exponents, and the effect of nonlinear stiffness was investigated. The nonlinear dynamic behaviors and characteristics of the FBEH demonstrate the consistent dynamic response patterns of the FBEH under different initial magnetic spacings, generally following the sequence of periodic intrawell oscillations, chaotic interwell oscillations, multi-orbit asymmetric periodic responses, chaotic responses and symmetric periodic responses. The initial magnetic spacing and nonlinear stiffness coefficients significantly influenced the jump frequency and response amplitude, whereas their impact on the dynamic response patterns was relatively minor. Overall, this study enhances the theoretical understanding of the FBEH in rotational environments by providing valuable insights and references for the design of such complex nonlinear electromechanical coupling systems.

对于具有时变势阱的双光束耦合柔性双稳能量采集器（FBEH）来说，利用多项式同时精确拟合两个方向的磁力是困难的，这阻碍了解析解的推导。因此，本研究采用增量谐波平衡法（IHBM）和弧长法相结合的半解析方法确定周期解，并用Floquet理论评估稳定性。对结构的动力响应进行了全面的分析，包括跳跃现象、多解和分岔特征。得到的半解析解对系统的周期响应有很好的近似。随后，通过李雅普诺夫指数分析了混沌响应，并研究了非线性刚度对混沌响应的影响。FBEH的非线性动力学行为和特征表明，在不同初始磁间距下，FBEH的动力学响应模式是一致的，一般遵循周期性井内振荡、混沌井间振荡、多轨道不对称周期响应、混沌响应和对称周期响应的顺序。初始磁间距和非线性刚度系数对跳频和响应幅值的影响显著，而对动态响应模式的影响相对较小。总体而言，本研究通过为此类复杂非线性机电耦合系统的设计提供有价值的见解和参考，增强了对旋转环境下FBEH的理论认识。

{"title":"Periodic and chaotic responses of flexible bistable energy harvesters in rotational environment","authors":"Suo Wang , He Ma , Zhiyuan Li , Houfan Du , Shengxi Zhou","doi":"10.1016/j.ijnonlinmec.2025.105264","DOIUrl":"10.1016/j.ijnonlinmec.2025.105264","url":null,"abstract":"<div><div>For the dual-beam coupled flexible bistable energy harvester (FBEH) with time-varying potential wells, accurately fitting the magnetic forces in two directions simultaneously using polynomials is difficult, hindering the derivation of the analytical solutions. Therefore, in this study, a semi-analytical method that combines the incremental harmonic balance method (IHBM) and the arc-length method is employed to determine the periodic solutions, with stability assessed by the Floquet theory. Comprehensive analyses of the dynamic responses are conducted, encompassing jump phenomenon, multiple solutions, and bifurcation characteristics. The obtained semi-analytical solutions demonstrate an excellent approximation for the system's periodic responses. Subsequently, the chaotic responses are analyzed via the Lyapunov exponents, and the effect of nonlinear stiffness was investigated. The nonlinear dynamic behaviors and characteristics of the FBEH demonstrate the consistent dynamic response patterns of the FBEH under different initial magnetic spacings, generally following the sequence of periodic intrawell oscillations, chaotic interwell oscillations, multi-orbit asymmetric periodic responses, chaotic responses and symmetric periodic responses. The initial magnetic spacing and nonlinear stiffness coefficients significantly influenced the jump frequency and response amplitude, whereas their impact on the dynamic response patterns was relatively minor. Overall, this study enhances the theoretical understanding of the FBEH in rotational environments by providing valuable insights and references for the design of such complex nonlinear electromechanical coupling systems.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105264"},"PeriodicalIF":3.2,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamic analysis and correlation propagation of the multibody system considering correlated interval parameters 考虑相关区间参数的多体系统动态分析及相关传播

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-09-13 DOI: 10.1016/j.ijnonlinmec.2025.105261

Xin Jiang, Qiang Zhang, Wenhan Cao, Xuqiang Dou

Interval uncertainty quantification for multibody systems has gained increasing attention due to complex requirements in the dynamic analysis of virtual prototypes. It is important to carefully consider the correlation between input interval parameters to avoid overestimating predictions, which can happen in traditional interval analysis that assumes parameters are mutually independent. This study introduced a new method that propagates multiple interval parameters with large uncertainty levels in multibody systems. The method combines local mean decomposition and bivariate function decomposition with Chebyshev polynomials to create a coupled surrogate model. This model can envelope the examined interval response and calculate response correlation coefficients. Numerical examples are provided to demonstrate the effectiveness of the method. The results showed that the proposed approach efficiently handles multiple interval parameters with significant uncertainty in the dynamic analysis of a multibody system.

由于虚拟样机动力学分析的复杂要求，多体系统的区间不确定性量化越来越受到人们的关注。重要的是仔细考虑输入区间参数之间的相关性，以避免高估预测，这可能发生在传统的区间分析中，假设参数是相互独立的。本文提出了一种在多体系统中传播具有大不确定度的多个区间参数的新方法。该方法将局部均值分解和二元函数分解与切比雪夫多项式相结合，建立耦合代理模型。该模型可以包络所测区间的响应并计算响应相关系数。数值算例验证了该方法的有效性。结果表明，该方法能有效地处理多体系统动力学分析中存在较大不确定性的多个区间参数。

引用次数: 0

Design of a piecewise-stiffening Nonlinear Energy Sink for torsional vibration attenuation 一种分段加强非线性减振能量池的设计

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-09-12 DOI: 10.1016/j.ijnonlinmec.2025.105248

Harikrishnan Venugopal, Mia Loccufier, Kevin Dekemele

Torsional vibrations are undesirable in rotating machinery, and demands for better performance and material savings to reduce weight exacerbate this issue by triggering resonance conditions. The Nonlinear Energy Sink (NES) offers a robust and effective vibration attenuation solution. In this research, a 2 Degree-Of-Freedom torsionally vibrating host structure is equipped with a NES having piecewise-linear stiffness approximating a cubic nonlinearity. The first-order Complexification-Averaging (CxA) method is used to analyse the Slow Flow dynamics on the response envelope, and a NES tuning methodology based on the Slow Invariant Manifold is proposed for 1:1 resonance attenuation for two resonance frequencies of the host system. The mechanical design of the NES is optimised for minimal stresses and fatigue while avoiding local resonances of the individual components. Experiments and numerical simulations validate the CxA method, and indicate the presence of Strongly Modulated Response regime and an Isolated Resonance Curve in the vicinity of resonance. Significant resonant response attenuation is achieved for both the first mode (

> 80 %

) and the second mode (

> 65 %

) over a wide range of forcing amplitudes, with possibility of further improvements. In this regard, design modifications that allow for effective multi-modal attenuation are presented. As such, a complete toolchain has been developed to obtain an NES design which can be applied to a wide range of torsional vibration applications.

在旋转机械中，扭转振动是不受欢迎的，为了减轻重量，需要更好的性能和节省材料，从而引发共振条件，从而加剧了这一问题。非线性能量汇（NES）提供了一种鲁棒和有效的振动衰减解决方案。在本研究中，一个2自由度扭振主体结构配备了一个具有近似三次非线性的分段线性刚度的NES。采用一阶复化平均（CxA）方法分析了响应包络上的慢流动力学，并提出了一种基于慢不变流形的主机系统两个共振频率1:1共振衰减的NES调谐方法。NES的机械设计针对最小应力和疲劳进行了优化，同时避免了单个组件的局部共振。实验和数值模拟验证了该方法的有效性，并表明在谐振区附近存在强调制响应区和孤立共振曲线。在很宽的强迫幅度范围内，第一模态（>80%）和第二模态（>65%）都实现了显著的谐振响应衰减，并有可能进一步改进。在这方面，提出了允许有效的多模态衰减的设计修改。因此，已经开发了一个完整的工具链，以获得一个NES设计，可以应用于广泛的扭转振动应用。

{"title":"Design of a piecewise-stiffening Nonlinear Energy Sink for torsional vibration attenuation","authors":"Harikrishnan Venugopal, Mia Loccufier, Kevin Dekemele","doi":"10.1016/j.ijnonlinmec.2025.105248","DOIUrl":"10.1016/j.ijnonlinmec.2025.105248","url":null,"abstract":"<div><div>Torsional vibrations are undesirable in rotating machinery, and demands for better performance and material savings to reduce weight exacerbate this issue by triggering resonance conditions. The Nonlinear Energy Sink (NES) offers a robust and effective vibration attenuation solution. In this research, a 2 Degree-Of-Freedom torsionally vibrating host structure is equipped with a NES having piecewise-linear stiffness approximating a cubic nonlinearity. The first-order Complexification-Averaging (CxA) method is used to analyse the Slow Flow dynamics on the response envelope, and a NES tuning methodology based on the Slow Invariant Manifold is proposed for 1:1 resonance attenuation for two resonance frequencies of the host system. The mechanical design of the NES is optimised for minimal stresses and fatigue while avoiding local resonances of the individual components. Experiments and numerical simulations validate the CxA method, and indicate the presence of Strongly Modulated Response regime and an Isolated Resonance Curve in the vicinity of resonance. Significant resonant response attenuation is achieved for both the first mode (<span><math><mrow><mo>></mo><mn>80</mn><mtext>%</mtext></mrow></math></span>) and the second mode (<span><math><mrow><mo>></mo><mn>65</mn><mtext>%</mtext></mrow></math></span>) over a wide range of forcing amplitudes, with possibility of further improvements. In this regard, design modifications that allow for effective multi-modal attenuation are presented. As such, a complete toolchain has been developed to obtain an NES design which can be applied to a wide range of torsional vibration applications.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105248"},"PeriodicalIF":3.2,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Periodic stochastic responses of nonlinear systems under combined harmonic and Poisson white noise excitations 谐波与泊松白噪声联合激励下非线性系统的周期随机响应

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-09-11 DOI: 10.1016/j.ijnonlinmec.2025.105253

Yuanyuan Bai, Liang Wang, Wei Xu

This study proposes a path integration framework to investigate the periodic response evolution of nonlinear dynamical systems subjected to combined harmonic and Poisson white noise excitations. To address the problem of sharp transition probability density functions induced by Poisson white noise, the variable substitution and mapping techniques are introduced to enhance the accuracy of the probability density function. For the periodic response analysis, a decomposition strategy is developed to reconstruct the multi-step transition probability density functions within a full period, deviating from the traditional single-step approach. These functions are subsequently incorporated into the Chapman–Kolmogorov equation for numerical iteration, enabling the derivation of time-dependent probability density functions for different period phases. The methodology is validated through two representative stochastic systems: one under external harmonic excitation and the other under parametric harmonic excitation. The underlying mechanism of two different excitation modes on the system response is discussed, and the correctness of the results is verified by comparing them with Monte Carlo simulation results.

本文提出了一个路径积分框架来研究在谐波和泊松白噪声联合激励下非线性动力系统的周期响应演化。针对泊松白噪声引起的突发性转移概率密度函数问题，引入变量替换和映射技术来提高概率密度函数的精度。针对周期响应分析，抛弃了传统的单步方法，提出了一种分解策略，在全周期内重构多步过渡概率密度函数。这些函数随后被纳入Chapman-Kolmogorov方程进行数值迭代，从而可以推导出不同周期阶段的随时间变化的概率密度函数。通过两个具有代表性的随机系统：一个是外部谐波激励，另一个是参数谐波激励，对该方法进行了验证。讨论了两种不同激励模式对系统响应的影响机理，并与蒙特卡罗仿真结果进行了对比，验证了结果的正确性。

{"title":"Periodic stochastic responses of nonlinear systems under combined harmonic and Poisson white noise excitations","authors":"Yuanyuan Bai, Liang Wang, Wei Xu","doi":"10.1016/j.ijnonlinmec.2025.105253","DOIUrl":"10.1016/j.ijnonlinmec.2025.105253","url":null,"abstract":"<div><div>This study proposes a path integration framework to investigate the periodic response evolution of nonlinear dynamical systems subjected to combined harmonic and Poisson white noise excitations. To address the problem of sharp transition probability density functions induced by Poisson white noise, the variable substitution and mapping techniques are introduced to enhance the accuracy of the probability density function. For the periodic response analysis, a decomposition strategy is developed to reconstruct the multi-step transition probability density functions within a full period, deviating from the traditional single-step approach. These functions are subsequently incorporated into the Chapman–Kolmogorov equation for numerical iteration, enabling the derivation of time-dependent probability density functions for different period phases. The methodology is validated through two representative stochastic systems: one under external harmonic excitation and the other under parametric harmonic excitation. The underlying mechanism of two different excitation modes on the system response is discussed, and the correctness of the results is verified by comparing them with Monte Carlo simulation results.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105253"},"PeriodicalIF":3.2,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Thermo-viscoplastic constitutive modeling of semicrystalline polymers with a novel perturbation-based return-mapping algorithm 基于微扰回归映射算法的半晶聚合物热粘塑性本构建模

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-09-10 DOI: 10.1016/j.ijnonlinmec.2025.105252

Rahele Vadizadeh , Asghar Zajkani , Mohsen Mirkhalaf

The elasto-viscoplastic behavior of semicrystalline polymers is modeled using an implicit finite element framework across three distinct temperature regimes: below, near, and above the glass transition temperature. The study considers varying strain rates under both isothermal and adiabatic conditions. A phenomenological DSGZ (Duan, Saigal, Greif, and Zimmerman) viscoplastic model is developed specifically for semi-crystalline thermoplastics with high thermal and mechanical resistances. To address the challenges of highly nonlinear terms, a novel perturbation-based return-mapping approach is introduced, ensuring stable and efficient stress integration. Additionally, an optimized procedure is seamlessly integrated to facilitate material parameter identification essential for the viscoplasticity model. Simulation results exhibit strong agreement with a wide range of experimental data, highlighting the necessity of temperature-specific parameter sets. Furthermore, a sensitivity analysis is conducted to assess the influence of key parameters on mechanical response. These findings establish a robust computational framework for accurately simulating and designing thermoplastic components subjected to complex thermo-mechanical loading scenarios.

半晶聚合物的弹粘塑性行为采用隐式有限元框架在三种不同的温度范围内建模：低于、接近和高于玻璃化转变温度。该研究考虑了在等温和绝热条件下不同的应变速率。DSGZ （Duan, Saigal, Greif, and Zimmerman）粘塑性模型是专门为具有高热阻和机械阻的半结晶热塑性塑料开发的。为了解决高度非线性项的挑战，引入了一种新的基于微扰的回归映射方法，以确保稳定和有效的应力积分。此外，优化程序无缝集成，以方便粘塑性模型必不可少的材料参数识别。模拟结果与广泛的实验数据表现出强烈的一致性，突出了温度特定参数设置的必要性。此外，还进行了灵敏度分析，以评估关键参数对力学响应的影响。这些发现为精确模拟和设计受复杂热机械载荷情景影响的热塑性部件建立了一个强大的计算框架。

{"title":"Thermo-viscoplastic constitutive modeling of semicrystalline polymers with a novel perturbation-based return-mapping algorithm","authors":"Rahele Vadizadeh , Asghar Zajkani , Mohsen Mirkhalaf","doi":"10.1016/j.ijnonlinmec.2025.105252","DOIUrl":"10.1016/j.ijnonlinmec.2025.105252","url":null,"abstract":"<div><div>The elasto-viscoplastic behavior of semicrystalline polymers is modeled using an implicit finite element framework across three distinct temperature regimes: below, near, and above the glass transition temperature. The study considers varying strain rates under both isothermal and adiabatic conditions. A phenomenological DSGZ (Duan, Saigal, Greif, and Zimmerman) viscoplastic model is developed specifically for semi-crystalline thermoplastics with high thermal and mechanical resistances. To address the challenges of highly nonlinear terms, a novel perturbation-based return-mapping approach is introduced, ensuring stable and efficient stress integration. Additionally, an optimized procedure is seamlessly integrated to facilitate material parameter identification essential for the viscoplasticity model. Simulation results exhibit strong agreement with a wide range of experimental data, highlighting the necessity of temperature-specific parameter sets. Furthermore, a sensitivity analysis is conducted to assess the influence of key parameters on mechanical response. These findings establish a robust computational framework for accurately simulating and designing thermoplastic components subjected to complex thermo-mechanical loading scenarios.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105252"},"PeriodicalIF":3.2,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A non-iterative method for nonlinear modal analysis of frictional systems using contact-state interpolation 基于接触状态插值的摩擦系统非线性模态分析的非迭代方法

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-09-09 DOI: 10.1016/j.ijnonlinmec.2025.105254

Yi Yao , Yanbin Lei , Louis Jézéquel , Xingrong Huang

This paper presents a non-iterative approximative nonlinear mode method based on linear modes for systems frictional stick-slip interfaces under the single resonant mode assumption. The proposed method effectively captures the influence of contact states on nonlinear dynamic behavior and addresses the need for efficient predictive analysis in frictionally damped systems. The core idea is to characterize contact states via stick-slip transitions at frictionally damped systems. Nonlinear modes are constructed by interpolating between linear modes associated with piecewise contact states, ranging from fully stuck to fully slipped. Under the weakly nonlinear assumption, interpolation functions for nonlinear modal frequencies are first established for one single frictional interface, and then generalized to multiple contact interfaces. The interpolation leverages linear modes across varying contact states to construct a piecewise function describing the dependency of nonlinear modal frequencies on relative displacement amplitudes on the interface. This non-iterative formulation avoids computationally expensive iterative procedures determining nonlinear frequencies. Moreover, corresponding nonlinear mode shapes are derived using the interpolated frequencies, and damping ratios are computed via an energy-based approach. The accuracy and efficiency of the proposed framework are demonstrated through three academic and one engineering numerical case studies.

在单共振模态假设下，提出了基于线性模态的系统粘滑摩擦界面非迭代近似非线性模态方法。该方法有效地捕捉了接触状态对非线性动力学行为的影响，解决了摩擦阻尼系统中高效预测分析的需求。核心思想是通过摩擦阻尼系统的粘滑过渡来表征接触状态。非线性模态是通过插值与分段接触状态相关的线性模态来构建的，从完全粘滞到完全滑动。在弱非线性假设下，首先针对单个摩擦界面建立非线性模态频率的插值函数，然后将其推广到多个接触界面。该插值利用不同接触状态下的线性模态来构造一个分段函数，该函数描述了非线性模态频率与界面上相对位移幅值的相关性。这种非迭代公式避免了计算昂贵的迭代过程来确定非线性频率。此外，利用插值频率推导了相应的非线性模态振型，并通过基于能量的方法计算了阻尼比。通过三个学术和一个工程数值算例验证了该框架的准确性和有效性。

{"title":"A non-iterative method for nonlinear modal analysis of frictional systems using contact-state interpolation","authors":"Yi Yao , Yanbin Lei , Louis Jézéquel , Xingrong Huang","doi":"10.1016/j.ijnonlinmec.2025.105254","DOIUrl":"10.1016/j.ijnonlinmec.2025.105254","url":null,"abstract":"<div><div>This paper presents a non-iterative approximative nonlinear mode method based on linear modes for systems frictional stick-slip interfaces under the single resonant mode assumption. The proposed method effectively captures the influence of contact states on nonlinear dynamic behavior and addresses the need for efficient predictive analysis in frictionally damped systems. The core idea is to characterize contact states via stick-slip transitions at frictionally damped systems. Nonlinear modes are constructed by interpolating between linear modes associated with piecewise contact states, ranging from fully stuck to fully slipped. Under the weakly nonlinear assumption, interpolation functions for nonlinear modal frequencies are first established for one single frictional interface, and then generalized to multiple contact interfaces. The interpolation leverages linear modes across varying contact states to construct a piecewise function describing the dependency of nonlinear modal frequencies on relative displacement amplitudes on the interface. This non-iterative formulation avoids computationally expensive iterative procedures determining nonlinear frequencies. Moreover, corresponding nonlinear mode shapes are derived using the interpolated frequencies, and damping ratios are computed via an energy-based approach. The accuracy and efficiency of the proposed framework are demonstrated through three academic and one engineering numerical case studies.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105254"},"PeriodicalIF":3.2,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145106002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bounded responses from a nonlinear model with mode-coupling instability and negative stiffness in one of its contact interfaces 具有模态耦合不稳定性和其中一个接触界面负刚度的非线性模型的有界响应

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-09-08 DOI: 10.1016/j.ijnonlinmec.2025.105237

Hugo Heidy Miyasato, Vinícius Gabriel Segala Simionatto, Milton Dias Junior

Mode coupling is a mechanism of friction-induced vibration that is considered one of the most relevant theories for studying brake squeal. This work introduced a negative stiffness effect in one of the contact interfaces from a nonlinear model with two degrees-of-freedom (DOF) and no external sources of damping. The linearized version presented multi-stability, where pure imaginary characteristic roots (i.e., marginal or neutral stability conditions) occurred for two points under specific parameter combinations. Besides, incommensurate natural frequency ratios prevail under those circumstances unless the exact parameter combinations are applied. Thus, an approximated two-frequency solution was developed using the Harmonic Balance Method (HBM) to evaluate which frequencies played the main role on the power exchanged at contact interfaces. The main results show that some of the marginally stable conditions produced quasi-periodic oscillations, where the liquid power exchanged (i.e. due to the oscillation of the system alone) was represented with important contributions of dominant frequency combinations. As a result, the total work exchanged varied in time as a bounded train of pulses.

模态耦合是一种摩擦诱发振动的机制，被认为是研究制动尖叫最相关的理论之一。这项工作从一个具有两个自由度（DOF）且没有外部阻尼源的非线性模型中引入了一个接触界面的负刚度效应。线性化版本呈现多重稳定性，在特定参数组合下，两点出现纯虚特征根（即边缘或中性稳定条件）。此外，在这些情况下，除非应用精确的参数组合，否则会出现不相称的固有频率比。因此，使用谐波平衡法（HBM）开发了一个近似的双频解，以评估哪些频率对接触界面上交换的功率起主要作用。主要结果表明，在某些边缘稳定条件下，系统产生了准周期振荡，其中液体功率的交换（即由于系统本身的振荡）由主导频率组合的重要贡献来表示。结果，交换的总功作为有界脉冲序列随时间变化。

{"title":"Bounded responses from a nonlinear model with mode-coupling instability and negative stiffness in one of its contact interfaces","authors":"Hugo Heidy Miyasato, Vinícius Gabriel Segala Simionatto, Milton Dias Junior","doi":"10.1016/j.ijnonlinmec.2025.105237","DOIUrl":"10.1016/j.ijnonlinmec.2025.105237","url":null,"abstract":"<div><div>Mode coupling is a mechanism of friction-induced vibration that is considered one of the most relevant theories for studying brake squeal. This work introduced a negative stiffness effect in one of the contact interfaces from a nonlinear model with two degrees-of-freedom (DOF) and no external sources of damping. The linearized version presented multi-stability, where pure imaginary characteristic roots (i.e., marginal or neutral stability conditions) occurred for two points under specific parameter combinations. Besides, incommensurate natural frequency ratios prevail under those circumstances unless the exact parameter combinations are applied. Thus, an approximated two-frequency solution was developed using the Harmonic Balance Method (HBM) to evaluate which frequencies played the main role on the power exchanged at contact interfaces. The main results show that some of the marginally stable conditions produced quasi-periodic oscillations, where the liquid power exchanged (i.e. due to the oscillation of the system alone) was represented with important contributions of dominant frequency combinations. As a result, the total work exchanged varied in time as a bounded train of pulses.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105237"},"PeriodicalIF":3.2,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Design and vibration isolation analysis of locally resonant metamaterial structures considering collision and stick-slip 考虑碰撞和粘滑的局部共振超材料结构设计与隔振分析

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-09-06 DOI: 10.1016/j.ijnonlinmec.2025.105256

Guofang Li , Xiaoli Ji , Shaopei Wu , Deyang Li , Jiqi Wang , Wangcai Ding

Metamaterials play a significant role in controlling wave propagation, and locally resonant metamaterial structures are widely used for vibration isolation. Therefore, this study considers discontinuous external environmental resistance and internal non-smooth collisions, and adopts a physical-to-mathematical modeling approach to build the physical model from a single-unit system to a multi-unit system. A locally resonant metamaterial structure consisting of a mass-spring-mass system with collisions and stick-slip effects is designed. Under a three-unit system, the switching mechanism is incorporated to validate and demonstrate the rationality and effectiveness of the motion behavior of the system. The wave transmission rate in the chain is obtained to reveal the wave propagation effects under different inter-unit parameter ratios. After optimizing the parameters, the number of units is varied to investigate the influence of unit quantity on wave transmission and vibration isolation performance. The research shows that increasing the inter-unit damping ratio, decreasing the inter-unit stiffness ratio, increasing the base mass ratio, decreasing the intra-unit stiffness ratio, and higher friction contribute to broadening the vibration isolation region and maintaining stable isolation. Parameter optimization and an increase in the number of units help achieve effective vibration isolation at lower frequencies, expand the isolation range, and promote wave attenuation. The research results provide a feasible approach for wave attenuation by adjusting inter-unit parameter ratios and the number of units.

超材料在控制波的传播中起着重要的作用，局部共振超材料结构被广泛用于隔振。因此，本研究考虑了不连续的外部环境阻力和内部的非光滑碰撞，采用物理到数学的建模方法，建立了从单单元系统到多单元系统的物理模型。设计了一种具有碰撞和粘滑效应的质量-弹簧-质量系统的局部共振超材料结构。在三单元系统下，加入切换机构，验证和论证了系统运动行为的合理性和有效性。得到了波在链中的传播速率，揭示了不同单元间参数比下的波传播效应。优化参数后，改变单元数量，研究单元数量对隔振性能和传波性能的影响。研究表明，增大单元间阻尼比、减小单元间刚度比、增大基质量比、减小单元间刚度比、增大摩擦力有助于拓宽隔振区域，保持隔振稳定。参数优化和单元数量的增加有助于实现低频有效隔振，扩大隔振范围，促进波的衰减。研究结果为调整单元间参数比和单元数进行波衰减提供了一种可行的方法。

{"title":"Design and vibration isolation analysis of locally resonant metamaterial structures considering collision and stick-slip","authors":"Guofang Li , Xiaoli Ji , Shaopei Wu , Deyang Li , Jiqi Wang , Wangcai Ding","doi":"10.1016/j.ijnonlinmec.2025.105256","DOIUrl":"10.1016/j.ijnonlinmec.2025.105256","url":null,"abstract":"<div><div>Metamaterials play a significant role in controlling wave propagation, and locally resonant metamaterial structures are widely used for vibration isolation. Therefore, this study considers discontinuous external environmental resistance and internal non-smooth collisions, and adopts a physical-to-mathematical modeling approach to build the physical model from a single-unit system to a multi-unit system. A locally resonant metamaterial structure consisting of a mass-spring-mass system with collisions and stick-slip effects is designed. Under a three-unit system, the switching mechanism is incorporated to validate and demonstrate the rationality and effectiveness of the motion behavior of the system. The wave transmission rate in the chain is obtained to reveal the wave propagation effects under different inter-unit parameter ratios. After optimizing the parameters, the number of units is varied to investigate the influence of unit quantity on wave transmission and vibration isolation performance. The research shows that increasing the inter-unit damping ratio, decreasing the inter-unit stiffness ratio, increasing the base mass ratio, decreasing the intra-unit stiffness ratio, and higher friction contribute to broadening the vibration isolation region and maintaining stable isolation. Parameter optimization and an increase in the number of units help achieve effective vibration isolation at lower frequencies, expand the isolation range, and promote wave attenuation. The research results provide a feasible approach for wave attenuation by adjusting inter-unit parameter ratios and the number of units.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105256"},"PeriodicalIF":3.2,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Unified model for shear strength of soft and hard rock masses based on in-Situ direct shear test parameters 基于原位直剪试验参数的软、硬岩体抗剪强度统一模型

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-09-06 DOI: 10.1016/j.ijnonlinmec.2025.105233

Shishu Zhang , Canlin Li , Congyan Ran , Zhanglei Wu , Weidong Deng , Haizhu Qu , Zhen Liu , Cuiying Zhou

The nonlinear evolution of rock mass shear strength and its coupling with structural plane morphology represent a critical scientific challenge in geotechnical stability analysis. Existing shear strength models based on in-situ direct shear tests lack universality for both soft and hard rock masses, failing to meet rapid stability assessment needs in engineering practice. To address this gap, the study improves the Mohr-Coulomb criterion by incorporating a normal stress modulation coefficient (κ) and a shear plane undulation coupling coefficient (λ). A unified shear strength model for soft-hard rock masses, accounting for normal stress effects, is proposed. The model's validity is confirmed using in-situ direct shear test data from engineering sites. The results demonstrate excellent fitting of experimental data. Hard rocks exhibit characteristics of normal stress suppression coupled with undulation enhancement, while soft rocks display normal stress strengthening and undulation weakening. Structural plane specimens exhibit normal stress inhibition resulting from plastic deformation, while residual interlocking maintains positive contributions from undulations. The model reveals the differential governing mechanisms of normal stress and shear plane undulation on shear strength in soft-hard interbedded rock masses, providing a theoretical foundation for rapid stability assessments in rock mass engineering.

岩体抗剪强度的非线性演化及其与结构面形态的耦合是岩土稳定性分析的重要科学挑战。现有的基于原位直剪试验的抗剪强度模型对软、硬岩体都缺乏通用性，不能满足工程实践中快速稳定性评价的需要。为了解决这一差距，该研究通过纳入法向应力调制系数（κ）和剪切面波动耦合系数（λ）来改进Mohr-Coulomb准则。提出了考虑正应力效应的软硬岩体统一抗剪强度模型。利用工程现场直剪试验数据，验证了模型的有效性。结果表明，该方法与实验数据拟合良好。硬岩表现为正应力抑制和波动增强的特征，软岩表现为正应力增强和波动减弱的特征。结构面试样表现出由塑性变形引起的正常应力抑制，而残余联锁保持波动的积极贡献。该模型揭示了软-硬互层岩体中正应力和剪切面波动对抗剪强度的差异调控机制，为岩体工程中快速稳定性评价提供了理论基础。

{"title":"Unified model for shear strength of soft and hard rock masses based on in-Situ direct shear test parameters","authors":"Shishu Zhang , Canlin Li , Congyan Ran , Zhanglei Wu , Weidong Deng , Haizhu Qu , Zhen Liu , Cuiying Zhou","doi":"10.1016/j.ijnonlinmec.2025.105233","DOIUrl":"10.1016/j.ijnonlinmec.2025.105233","url":null,"abstract":"<div><div>The nonlinear evolution of rock mass shear strength and its coupling with structural plane morphology represent a critical scientific challenge in geotechnical stability analysis. Existing shear strength models based on in-situ direct shear tests lack universality for both soft and hard rock masses, failing to meet rapid stability assessment needs in engineering practice. To address this gap, the study improves the Mohr-Coulomb criterion by incorporating a normal stress modulation coefficient (<em>κ</em>) and a shear plane undulation coupling coefficient (<em>λ</em>). A unified shear strength model for soft-hard rock masses, accounting for normal stress effects, is proposed. The model's validity is confirmed using in-situ direct shear test data from engineering sites. The results demonstrate excellent fitting of experimental data. Hard rocks exhibit characteristics of normal stress suppression coupled with undulation enhancement, while soft rocks display normal stress strengthening and undulation weakening. Structural plane specimens exhibit normal stress inhibition resulting from plastic deformation, while residual interlocking maintains positive contributions from undulations. The model reveals the differential governing mechanisms of normal stress and shear plane undulation on shear strength in soft-hard interbedded rock masses, providing a theoretical foundation for rapid stability assessments in rock mass engineering.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105233"},"PeriodicalIF":3.2,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A novel variable fractional constitutive model for complex multistage polymeric behaviors 复杂多级聚合物行为的一种新的可变分数本构模型

IF 3.2 3区工程技术 Q2 MECHANICS

International Journal of Non-Linear Mechanics

Pub Date : 2025-09-06 DOI: 10.1016/j.ijnonlinmec.2025.105255

Leixiao Wu, Wei Cai, Zhouquan Wang, Jie Yang

The mechanical behaviors of glassy polymers, including the viscoelastic and viscoplastic phases, are highly sensitive to temperature and strain rate. In order to describe such complex stress-strain responses, a variable fractional constitutive model considering temperature and strain rate effects is proposed with the order characterized by a biexponential function. Temperature and strain rate dependent criterion are established for both the elastic modulus and relaxation time, which are linearly decreasing functions of temperature. The fractional orders at different temperatures can be described by the same biexponential function, independent of temperature and strain rate, which indicates the same evolution trend during loading. The unloading behavior is subsequently characterized by shifting the order function depending on the reference unload strain. Numerical simulations show that the proposed model well describes and predicts the loading and unloading behaviors of glassy polymers. The physical interpretation of the order evolution is revealed based on the molecular chain mechanism. The validity and applicability of the model is further verified by the application of the model to different glassy polymers.

玻璃聚合物的力学行为，包括粘弹性阶段和粘塑性阶段，对温度和应变速率高度敏感。为了描述这种复杂的应力-应变响应，提出了考虑温度和应变率影响的变分数本构模型，其阶数以双指数函数为特征。建立了弹性模量和松弛时间随温度线性递减的温度和应变率判据。不同温度下的分数阶可以用相同的双指数函数来描述，与温度和应变速率无关，表明加载过程中的演化趋势相同。卸载行为随后通过根据参考卸载应变改变阶函数来表征。数值模拟结果表明，该模型能较好地描述和预测玻璃聚合物的加载和卸载行为。基于分子链机制，揭示了有序演化的物理解释。将该模型应用于不同的玻璃聚合物，进一步验证了该模型的有效性和适用性。

{"title":"A novel variable fractional constitutive model for complex multistage polymeric behaviors","authors":"Leixiao Wu, Wei Cai, Zhouquan Wang, Jie Yang","doi":"10.1016/j.ijnonlinmec.2025.105255","DOIUrl":"10.1016/j.ijnonlinmec.2025.105255","url":null,"abstract":"<div><div>The mechanical behaviors of glassy polymers, including the viscoelastic and viscoplastic phases, are highly sensitive to temperature and strain rate. In order to describe such complex stress-strain responses, a variable fractional constitutive model considering temperature and strain rate effects is proposed with the order characterized by a biexponential function. Temperature and strain rate dependent criterion are established for both the elastic modulus and relaxation time, which are linearly decreasing functions of temperature. The fractional orders at different temperatures can be described by the same biexponential function, independent of temperature and strain rate, which indicates the same evolution trend during loading. The unloading behavior is subsequently characterized by shifting the order function depending on the reference unload strain. Numerical simulations show that the proposed model well describes and predicts the loading and unloading behaviors of glassy polymers. The physical interpretation of the order evolution is revealed based on the molecular chain mechanism. The validity and applicability of the model is further verified by the application of the model to different glassy polymers.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"180 ","pages":"Article 105255"},"PeriodicalIF":3.2,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145020075","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0