International Journal of Non-Linear Mechanics最新文献

{"title":"Design of a piecewise-stiffening Nonlinear Energy Sink for torsional vibration attenuation","authors":"Harikrishnan Venugopal,&nbsp;Mia Loccufier,&nbsp;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>&gt;</mo><mn>80</mn><mtext>%</mtext></mrow></math></span>) and the second mode (<span><math><mrow><mo>&gt;</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}

{"title":"Periodic stochastic responses of nonlinear systems under combined harmonic and Poisson white noise excitations","authors":"Yuanyuan Bai,&nbsp;Liang Wang,&nbsp;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}

{"title":"Thermo-viscoplastic constitutive modeling of semicrystalline polymers with a novel perturbation-based return-mapping algorithm","authors":"Rahele Vadizadeh ,&nbsp;Asghar Zajkani ,&nbsp;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}

{"title":"A non-iterative method for nonlinear modal analysis of frictional systems using contact-state interpolation","authors":"Yi Yao ,&nbsp;Yanbin Lei ,&nbsp;Louis Jézéquel ,&nbsp;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}

{"title":"Bounded responses from a nonlinear model with mode-coupling instability and negative stiffness in one of its contact interfaces","authors":"Hugo Heidy Miyasato,&nbsp;Vinícius Gabriel Segala Simionatto,&nbsp;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}

{"title":"Design and vibration isolation analysis of locally resonant metamaterial structures considering collision and stick-slip","authors":"Guofang Li ,&nbsp;Xiaoli Ji ,&nbsp;Shaopei Wu ,&nbsp;Deyang Li ,&nbsp;Jiqi Wang ,&nbsp;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}

{"title":"Unified model for shear strength of soft and hard rock masses based on in-Situ direct shear test parameters","authors":"Shishu Zhang ,&nbsp;Canlin Li ,&nbsp;Congyan Ran ,&nbsp;Zhanglei Wu ,&nbsp;Weidong Deng ,&nbsp;Haizhu Qu ,&nbsp;Zhen Liu ,&nbsp;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}

{"title":"A novel variable fractional constitutive model for complex multistage polymeric behaviors","authors":"Leixiao Wu,&nbsp;Wei Cai,&nbsp;Zhouquan Wang,&nbsp;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}

{"title":"Free vibrations of an elastica around its post-buckled configurations","authors":"H. Kibach,&nbsp;A. Ture Savadkoohi,&nbsp;C.-H. Lamarque","doi":"10.1016/j.ijnonlinmec.2025.105250","DOIUrl":"10.1016/j.ijnonlinmec.2025.105250","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105250"},"PeriodicalIF":3.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988184","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}

{"title":"Comprehending stability and bifurcations in Mathieu cubic–quintic Duffing system using Lindstedt–Poincaré methodology","authors":"Abhik Mukherjee ,&nbsp;Anurag","doi":"10.1016/j.ijnonlinmec.2025.105236","DOIUrl":"10.1016/j.ijnonlinmec.2025.105236","url":null,"abstract":"<div><div>The Mathieu equation serves as a foundational model in the study of parametrically excited systems and has been extensively analyzed using both analytical and numerical techniques. Motivated by its relevance to various physical and engineering systems, we investigate its nonlinear extension – the Mathieu cubic–quintic Duffing equation – which includes both cubic and quintic stiffness terms. This nonlinear variant exhibits rich dynamical behavior including complex stability transitions and bifurcations. To explore these phenomena, we employ the Lindstedt–Poincaré method, which allows us to analytically capture both pitchfork bifurcations (subcritical and supercritical) near unstable parametric resonance tongues and subharmonic bifurcations at higher values of excitation frequencies. The analytical predictions are validated using numerical simulations based on Poincaré sections. Our results reveal the emergence of two distinct unstable tongues centered around <span><math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><msub><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn>2</mn><msub><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span>, as well as two subharmonic bifurcations located at <span><math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn>4</mn><msub><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mn>6</mn><msub><mrow><mi>ω</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span>. We construct a comprehensive global bifurcation diagram in the parametric frequency–excitation strength space, showing transitions in equilibrium stability and the birth of multiple stable and unstable equilibrium points. Notably, the transition through each bifurcation boundary results in a specific number of stable and unstable equilibrium points alternatively. These findings not only extend the known behavior of the Mathieu and Mathieu–Duffing systems but also offer deeper insight into the complex dynamics induced by higher-order nonlinearities.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"179 ","pages":"Article 105236"},"PeriodicalIF":3.2,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921168","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}