International Journal of Non-Linear Mechanics最新文献

{"title":"A Rayleigh–Ritz formulation of the Wiener path integral technique for high-dimensional nonlinear systems","authors":"Ketson R.M. dos Santos ,&nbsp;Ilias G. Mavromatis ,&nbsp;Ioannis A. Kougioumtzoglou","doi":"10.1016/j.ijnonlinmec.2026.105323","DOIUrl":"10.1016/j.ijnonlinmec.2026.105323","url":null,"abstract":"<div><div>A novel Rayleigh–Ritz-based formulation of the Wiener path integral (WPI) technique is developed for efficiently determining the stochastic response of high-dimensional nonlinear systems while circumventing the related “curse of dimensionality.” Specifically, based on the standard WPI formulation, the system response transition joint probability density function (PDF) is expressed as a functional integral over all paths satisfying the prescribed initial and final conditions of the response process. Typically, this functional integral is approximated based on the most probable path, which is obtained by solving a functional minimization problem that takes the form of Euler–Lagrange equations. While recent variational formulations allow direct computation of lower-dimensional PDFs, they require cumbersome symbolic-numerical implementations. To address this challenge, an alternative methodology is developed herein that transforms the original functional minimization problem into a standard finite-dimensional optimization problem, readily solvable with various well-established numerical schemes. In this regard, the need for deriving and solving Euler–Lagrange equations with complex boundary conditions is eliminated. Moreover, high-performance computing strategies, including GPU parallelization, are employed to further enhance the computational efficiency of the technique. A representative example is considered relating to a 1000-DOF nonlinear nano-mechanical system under stochastic excitation. The estimated response PDFs based on the WPI technique show excellent agreement with Monte Carlo simulations. These results highlight that the developed technique can accurately and efficiently handle truly high-dimensional nonlinear systems, paving the way for practical probabilistic analyses and uncertainty quantification in complex engineering applications.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"185 ","pages":"Article 105323"},"PeriodicalIF":3.2,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146045203","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":"Topological manifold versus multidirectional wall shear stress FSI approaches for the right coronary artery","authors":"Farajollah Zare Jouneghani,&nbsp;Mergen H. Ghayesh","doi":"10.1016/j.ijnonlinmec.2026.105319","DOIUrl":"10.1016/j.ijnonlinmec.2026.105319","url":null,"abstract":"<div><div>To date, researchers in the field of biomechanics have used various wall shear stress-based parameters to analyse hemodynamics to improve the medical understanding of atherosclerosis. In this paper, we aim to provide a comprehensive comparison between commonly used <em>multidirectional</em> and <em>topological skeleton</em> variables for a complex, patient-specific model of the right coronary artery (RCA) via a two-phase fluid-structure interaction (FSI) technique. To better replicate the real physiological conditions, a two-phase blood flow, comprising plasma and red blood cells, is considered. Additionally, a hyperelastic behaviour is defined for the RCA structure to represent the mechanical properties of human coronary arteries. Boundary conditions, including the velocity of blood components at the inlet and arterial wall motion, are configured based on in vivo data available in the literature. To identify regions prone to atherosclerosis and assess arterial vulnerability, recent studies have primarily focused on <em>multidirectional</em> wall shear stress (WSS) parameters. However, comparatively little attention has been given to <em>topological</em> hemodynamic features. In this work, we first derived the time averaged wall shear stress (TAWSS) and oscillatory shear index (OSI) as representatives of the multidirectional WSS, and WSS divergence and fixed points as representatives of the topological hemodynamics, and analysed them to evaluate arterial vulnerability. Among the main findings, this study shows that although both multidirectional and topology-skeleton metrics co-localise vulnerable regions of the artery, WSS divergence, as a topology-skeleton index, identifies these areas in a fragmented and localised manner. This represents a step toward defining more precise vulnerable zones in the cardiovascular system and predicting high-risk regions with greater accuracy.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"183 ","pages":"Article 105319"},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079372","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":"Dynamic analysis of multiple response patterns in a flexible multibody system with hybrid uncertainties","authors":"Jingwei Meng ,&nbsp;Yanfei Jin ,&nbsp;Haiyan Hu","doi":"10.1016/j.ijnonlinmec.2026.105318","DOIUrl":"10.1016/j.ijnonlinmec.2026.105318","url":null,"abstract":"<div><div>Multibody systems are often subject to multiple sources of uncertainty, including both random and interval types. The dynamic response of such a multibody system may exhibit multiple patterns that traditional surrogate modeling methods fail to capture effectively. To address this issue, this paper presents a hierarchical hybrid Kriging modeling approach for accurately predicting the multiple dynamic response patterns in a flexible multibody system with hybrid uncertainties. The approach employs adaptive <em>K</em>-means clustering to automatically identify the dynamic response patterns, assigning the inner-layer random samples and their dynamic responses to respective clusters under fixed outer-layer intervals. Following this assignment, variance-based sequential sampling augments the sample sets. The paper details the hierarchical hybrid Kriging model for each pattern, where the inner-layer model captures the influence of random uncertainties on the dynamic response, and the outer-layer model characterizes the propagation of interval uncertainties into the response mean and variance. This integrated process enables high-fidelity modeling and reliable prediction of multiple dynamic response patterns. Two classic examples demonstrate the high accuracy and computational efficiency of the method, which needs only 0.28 % of the computation time of the Monte Carlo-Scanning method.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"183 ","pages":"Article 105318"},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038907","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":"Analysis of arterial wall mechanics in right coronary artery obstructive disease: FSI modelling and non-invasive FFR validation","authors":"C. Paz ,&nbsp;F.P. Oliveira ,&nbsp;E. Suárez ,&nbsp;C. Gil ,&nbsp;N.D. Ferreira ,&nbsp;D. Santos-Ferreira ,&nbsp;R. Ladeiras-Lopes ,&nbsp;N. Bettencourt ,&nbsp;S.I.S. Pinto","doi":"10.1016/j.ijnonlinmec.2026.105320","DOIUrl":"10.1016/j.ijnonlinmec.2026.105320","url":null,"abstract":"<div><div>Coronary artery disease remains one of the principal causes of mortality worldwide, motivating the development of patient-specific computational frameworks capable of accurately characterizing arterial wall mechanics in obstructive right coronary artery disease. In this study, a Fluid–Structure Interaction (FSI) modelling approach was employed to capture the dynamic interplay between pulsatile blood flow and vascular wall behaviour, with validation against invasive fractional flow reserve (FFR) measurements to ensure a faithful reproduction of patient-specific physiological conditions. Numerical simulations were performed using one-way coupled FSI on patient-specific right coronary artery geometries reconstructed from computed tomography angiography data. Blood rheology was described using the simplified Phan-Thien/Tanner (sPTT) viscoelastic model, while realistic physiological loading was achieved through patient-specific hyperemic conditions, Womersley velocity profiles prescribed at the inlet, and three-element Windkessel models applied at the outlets. The analysis focused on the spatial distribution and magnitude of arterial wall stresses and deformations. Results showed that regions of elevated mechanical response consistently co-located with areas of significant pressure drop and stenosis. Quantitatively, maximum wall deformation varied markedly across patients, ranging from approximately 0.14 mm–0.39 mm, while maximum equivalent stress values ranged from about 40 kPa to over 80 kPa, highlighting strong inter-patient variability driven by individual anatomy and stenosis severity. Statistical analyses confirmed that these differences were significant, indicating a link between functional severity and mechanical loading of the arterial wall. Four stress- and deformation-based metrics exhibited strong correlations with clinically measured FFR values, with absolute correlation coefficients exceeding 0.5. Overall, the proposed patient-specific FSI framework enables a physiologically grounded characterization of arterial wall mechanics in obstructive right coronary artery disease, providing mechanistic insight into patient-specific coronary pathology.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"183 ","pages":"Article 105320"},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038950","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":"Frictional mass in mass based device for vibration control in railway tracks: An analytical and experimental investigation","authors":"Muskaan Sethi,&nbsp;Arnab Banerjee,&nbsp;Bappaditya Manna","doi":"10.1016/j.ijnonlinmec.2025.105311","DOIUrl":"10.1016/j.ijnonlinmec.2025.105311","url":null,"abstract":"<div><div>This manuscript presents a novel frictional mass in mass based device for vibration control in railway tracks. The proposed device comprises of an outer mass, which is rigidly clamped to the sleepers. The inner mass vibrates and rubs against the outer mass when the latter is subjected to an external excitation due to motion of a train over the railway track. As a result, frictional force is induced at the interface of both the masses, which leads to energy dissipation and helps in vibration control. The feasibility of proposed device for effective vibration control is thoroughly investigated by both analytical and experimental studies. For analytical study, an LCP based solver is discussed and presented to model a suitable frictional contact for the proposed device. An on field experimental study is further conducted to check the suitability of proposed device in effective vibration control in railway tracks. Both the analytical and experimental results prove that the proposed device can be a promising solution for effective vibration control in various components of railway track.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"183 ","pages":"Article 105311"},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145908888","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":"Stochastic response and dynamic reliability analysis of metro vehicle-track system with multi-source uncertainties","authors":"Jun Lai ,&nbsp;Zihan Zhou ,&nbsp;Tao Liao ,&nbsp;Yuan Li ,&nbsp;Jingmang Xu ,&nbsp;Kai Wang ,&nbsp;Ping Wang","doi":"10.1016/j.ijnonlinmec.2026.105316","DOIUrl":"10.1016/j.ijnonlinmec.2026.105316","url":null,"abstract":"<div><div>The combination of multi-source uncertainties of metro vehicle-track system (MVTS) can lead to nonlinear stochastic dynamic responses and further display random behaviour to failure of vehicles and tracks. However, no studies have considered the influence of multi-source uncertainties of out-of-roundness (OOR) wheels, track irregularities, and random variables on stochastic dynamic responses and the reliability of the MVTS. In this paper, we propose an efficient probabilistic-based framework to evaluate the failure probability of the train derailment and ride comfort considering wheelset flexibility. First, stochastic OOR wheels and track irregularities sequences are generated by physical random functions. Then, a metro vehicle-track coupled dynamic interaction model is established. Finally, the stochastic dynamic response and dynamic reliability analysis of MVTS are conducted based on direct probability integration method. The influence of the evolution of rail wear and the radius of curves on the dynamic reliability of MVTS has been explored in detail. The results show that the combined action of random OOR wheels and random track irregularities is greater than a single excitation. As the wear depth of the rail increases, the influence of uncertain inputs becomes more significant, and the dynamic reliability of the MVTS reduces to 0.86. Moreover, when the curve radius is 200 m, the reliability of the derailment coefficient can be maintained at a high level, while the reliability of ride comfort is reduced to 0.855.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"183 ","pages":"Article 105316"},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146079373","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":"Theoretical and experimental analysis of the synchronization bandwidth in nonlinear coupled micromechanical resonators","authors":"Zhonghua Liu ,&nbsp;Hang Yu ,&nbsp;Qiangfeng Lv ,&nbsp;Ronghua Huan","doi":"10.1016/j.ijnonlinmec.2026.105317","DOIUrl":"10.1016/j.ijnonlinmec.2026.105317","url":null,"abstract":"<div><div>The synchronization phenomenon has broad application prospects and has been employed in the design of micro-electromechanical systems (MEMS) devices such as accelerometers and gyroscopes. As a key parameter directly related to the measurement range, the synchronization bandwidth plays a crucial role but also limits the wider application of synchronization. In this work, we investigate the synchronization bandwidth of coupled micro-mechanical resonators with a 1:3 frequency ratio under stochastic perturbations. A theoretical model incorporating feedback strength, higher-order nonlinearity, electrostatic coupling, and external noise is first established. Based on the stochastic averaging method, analytical expressions for the synchronization bandwidth are derived for both noise-free and weak-noise cases, revealing the influence of various parameters on the bandwidth. A pair of coupled resonators with a 1:3 frequency ratio is then designed and fabricated. The experimental results indicate that increasing the coupling strength, disturbance intensity, and feedback strength can enhance the synchronization bandwidth, whereas an increase in noise intensity leads to a reduction in the synchronization bandwidth. The experimental results verify the correctness and effectiveness of the proposed theoretical approach.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"183 ","pages":"Article 105317"},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980918","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":"Study on broadband vibration energy harvesting mechanism via 1:2 internal resonance in a disc-shaped frequency upconverting resonator","authors":"Haiyang Zhao ,&nbsp;Meile Wang ,&nbsp;Yikun Liu ,&nbsp;Yangyang Yan ,&nbsp;Han Gao ,&nbsp;Jie Song ,&nbsp;Dan Ma ,&nbsp;Yuanlin Xia ,&nbsp;Dong F. Wang ,&nbsp;Zhuqing Wang ,&nbsp;Cao Xia","doi":"10.1016/j.ijnonlinmec.2026.105321","DOIUrl":"10.1016/j.ijnonlinmec.2026.105321","url":null,"abstract":"<div><div>As a novel energy harvesting device, the vibration energy harvester (VEH) uniquely converts ambient vibration energy into useable electrical energy for various applications. Environmental vibrations lack fixed sources, resulting in an extremely wide and random frequency bandwidth. If the VEH's natural frequency does not align with the environmental vibration frequency band, the energy harvesting efficiency decreases. Thus, the frequency bandwidth is crucial for energy harvesting efficiency. To address these challenges, this paper summarizes the mechanisms for expanding frequency bandwidth and proposes a high-filling-rate, disc-shaped VEH based on a 1:2 internal resonance with magnetic bias. By introducing a constant magnetic field, the structural symmetry is altered, and a quadratic nonlinear coupling stiffness is introduced to achieve internal coupling of the first two out-of-plane modes. The nonlinear dynamic motion equations are derived to predict the coupled behavior of the energy harvester. Numerical and experimental results indicate that the peak-splitting effect of the 1:2 internal resonance can bidirectionally widen the relative bandwidth of vibrational energy harvesting, with a 200 % increase in signal output frequency owing to frequency up-conversion. In addition, the proposed disc-shaped VEH with a high filling rate and two-dimensional spatial structures is also beneficial to improve the energy capture rate per unit area and reduce the volume of the energy harvester. It can be highly integrated into wireless sensor network nodes through MEMS technology.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"183 ","pages":"Article 105321"},"PeriodicalIF":3.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038949","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":"Passive energy redirection in a phononic lattice network through nonlinear wave scattering mechanisms","authors":"Anargyros Michaloliakos ,&nbsp;Aryan Arora ,&nbsp;Lawrence A. Bergman ,&nbsp;Alexander F. Vakakis","doi":"10.1016/j.ijnonlinmec.2025.105306","DOIUrl":"10.1016/j.ijnonlinmec.2025.105306","url":null,"abstract":"<div><div>This work investigates passive energy redirection in a network of coupled phononic lattices enabled by nonlinear scattering mechanisms that arise from the synergy of geometric and vibro-impact nonlinearities in optimized internal resonators. Unlike linear lattices, where wave propagation is governed solely by dispersion relations, the incorporation of localized nonlinear features facilitates amplitude and frequency dependent energy transfers in a priori selected pathways. In particular, we show how energy induced by incoming wave packets with varying central frequencies is preferentially redirected into a selected pathway (lattice) solely based on its frequency content. This enables frequency-selective passive routing without the need for active control. Wavelet-based signal processing, integrated with an energy management methodology, is employed to quantify and interpret the redistribution of wave energy across the time–frequency domain. To address the optimization of directed energy transfer in the high-dimensional design space of this phononic system, we employ a multi-objective genetic algorithm (MOGA) to optimize key system parameters. This yields Pareto-optimal solutions that capture the trade-offs between competing redirection objectives. This study confirms the effectiveness of nonlinear scattering through the synergy of internal resonance, vibro-impacts, and geometric nonlinearities in enabling robust and efficient passive energy control. These results point toward new opportunities for vibration mitigation, energy harvesting, targeted energy transfer, and effective wave manipulation in phononic and acoustic metamaterials.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"182 ","pages":"Article 105306"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145711770","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":"An improved high-order finite element method for nonlinear vibration of a rotating flexible hub-beam","authors":"Z.Z. Liu,&nbsp;J.L. Huang","doi":"10.1016/j.ijnonlinmec.2025.105308","DOIUrl":"10.1016/j.ijnonlinmec.2025.105308","url":null,"abstract":"<div><div>This work investigates the nonlinear chordwise vibration characteristics of a rotating flexible hub-beam under gravitational loading using an improved high-order finite element (HFE) method. A geometrically exact dynamic model is established using slope angle variables and Hamilton’s principle, incorporating geometric nonlinearity, rotational effects (Coriolis force, centrifugal force, and rotational inertia), and material damping. The model is discretized using the HFE method with an improved integration element technique that subdivides each finite element into sub-elements to precompute integral values at their nodes. Subsequently, a piecewise Hermite interpolation is employed to obtain integral values over the element. This method effectively eliminates computationally intensive double integrals and enhances efficiency without compromising accuracy. Validation through a flexible pendulum example demonstrates the high accuracy and computational efficiency of the method. The Incremental Harmonic Balance (IHB) method is employed to analyze the nonlinear periodic responses of the rotating flexible hub-beam, while the Floquet theory is utilized to assess stability of these periodic solutions. The analysis reveals rich nonlinear phenomena, including jump phenomena, period-doubling bifurcations, subharmonic and superharmonic resonances. Parametric studies further indicate that increased beam length or reduced damping intensifies nonlinear effects, whereas a larger hub radius enhances stiffness, raises resonance frequencies, and suppresses bifurcations, though expanding instability regions at higher frequencies.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"182 ","pages":"Article 105308"},"PeriodicalIF":3.2,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145841017","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}