International Journal of Non-Linear Mechanics最新文献

{"title":"Identification of nonlinear joints using amplitude-dependent modal parameters with high-accuracy reduction techniques","authors":"Xinliang Fan ,&nbsp;Tong Wang ,&nbsp;Bin Zhou","doi":"10.1016/j.ijnonlinmec.2025.105155","DOIUrl":"10.1016/j.ijnonlinmec.2025.105155","url":null,"abstract":"<div><div>An efficient identification method using amplitude-dependent modal parameters is developed for systems with nonlinear joints. In this method, the nonlinear modal parameters of lightly damped systems are calculated by the extension of the periodic motion concept (EPMC). First, an exact reduction technique is applied to reduce computational effort due to the sparsity of the nonlinear force. Next, the frequency response function (FRF) matrix of the linear part is approximated using the incremental modal expansion, achieving high accuracy to speed up the solution process. An approach to identifying the parameters of the joint model is then introduced, which utilizes the EPMC and the reduction techniques. The objective function for minimization is calculated as a function of the errors between the calculated and measured nonlinear modal parameters, and the corresponding sensitivity matrix is derived. In this work, the modal motion amplitude of a certain reference degree of freedom (DOF) is used as a reference quantity to match the calculated and measured data in the identification process. The efficiency and convergence of the identification method are validated through both simulated and experimental case studies. Results indicate that the identification method can be successfully applied to practical assembly structures.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"177 ","pages":"Article 105155"},"PeriodicalIF":2.8,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144108243","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":"Reduced-order modelling of parameter-dependent systems with invariant manifolds: Application to Hopf bifurcations in follower force problems","authors":"André de Figueiredo Stabile ,&nbsp;Alessandra Vizzaccaro ,&nbsp;Loïc Salles ,&nbsp;Alessio Colombo ,&nbsp;Attilio Frangi ,&nbsp;Cyril Touzé","doi":"10.1016/j.ijnonlinmec.2025.105133","DOIUrl":"10.1016/j.ijnonlinmec.2025.105133","url":null,"abstract":"<div><div>The direct parametrisation method for invariant manifolds is adjusted to consider a varying parameter. More specifically, the case of systems experiencing a Hopf bifurcation in the parameter range of interest is investigated, and the ability to predict the amplitudes of the limit cycle oscillations after the bifurcation is demonstrated. The cases of the Ziegler pendulum and Beck’s column, both of which have a follower force, are considered for applications. By comparison with the eigenvalue trajectories in the conservative case, it is advocated that using two master modes to derive the ROM, instead of only considering the unstable one, should give more accurate results. Also, in the specific case where an exceptional bifurcation point is met, a numerical strategy enforcing the presence of Jordan blocks in the Jacobian matrix during the procedure is devised. The ROMs are constructed for the Ziegler pendulum having two and three degrees of freedom, and then Beck’s column is investigated, where a finite element procedure is used to spatially discretise the problem. The numerical results show the ability of the ROMs to correctly predict the amplitude of the limit cycles up to a certain range, and it is shown that computing the ROM after the Hopf bifurcation gives the most satisfactory results. This feature is analysed in terms of phase space representations, and the two proposed adjustments are shown to improve the validity range of the ROMs.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"177 ","pages":"Article 105133"},"PeriodicalIF":2.8,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941226","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":"Development of a high-fidelity and optimal model for magneto-rheological damper by parametric sensitivity analysis","authors":"S. Adarsh ,&nbsp;Jagajyoti Panda ,&nbsp;Samit Ray-Chaudhuri","doi":"10.1016/j.ijnonlinmec.2025.105128","DOIUrl":"10.1016/j.ijnonlinmec.2025.105128","url":null,"abstract":"<div><div>This paper develops a high-fidelity and optimal mathematical model for the magneto-rheological (MR) damper, a popular semiactive control device, that can overcome the generic shortcomings of the existing parametric models, such as complex identification and simulation processes. A rigorous sensitivity analysis was performed using tornado diagrams and Monte Carlo simulations to reduce the number of parameters in the modified Bouc–Wen model with 21 amplitude and current parameters. Before the sensitivity analysis, a detailed experimental study with a laboratory-scale MR damper was performed to obtain its nonlinear hysteretic behavior through a series of displacement-controlled tests. From the results of the sensitivity analyses and exhaustive search, it was observed that the optimal Bouc–Wen model perfectly captured the nonlinear force–displacement and force–velocity behaviors of the damper. Moreover, the parameter identification results obtained using a genetic algorithm confirmed that the accuracy of the optimal model was the same as that of the original modified Bouc–Wen model, and the average simulation time of 1000 iterations was reduced considerably by up to 56% in the identified optimal model case. Finally, a numerical study was conducted on a multi-degree-of-freedom base-isolated building to evaluate the ability of the optimal model to simulate accurately the experimentally obtained nonlinear behavior of an MR damper. Additionally, the analysis results reinforce the broader use of mathematical models in the semiactive vibration control of structural systems.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"177 ","pages":"Article 105128"},"PeriodicalIF":2.8,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143918421","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":"Stress and friction evolution in the bolt during and after assembly","authors":"Zhixiang Li,&nbsp;Zhen Zhao,&nbsp;Qingyun Wang,&nbsp;Jiaying Zhang","doi":"10.1016/j.ijnonlinmec.2025.105132","DOIUrl":"10.1016/j.ijnonlinmec.2025.105132","url":null,"abstract":"<div><div>The stress distribution within threaded connections exhibits significant complexity attributable to the intricate interfacial friction between mating surfaces, which critically influences the coupled relationship among tightening torque, rotational angle, and axial preload. This study establishes a comprehensive assembly analytical framework incorporating three critical factors: thread contact deformation, screw body distortion, and frictional distribution evolution during and after assembly processes. Through this model, three distinct deformation patterns and corresponding stress distribution characteristics in bolted joints have been systematically identified. Subsequent numerical simulations quantitatively reveal the generation mechanisms of these stress patterns under varying operational conditions. Particularly, parametric analysis demonstrates that reduced stiffness of clamped components amplifies both rotational displacement and axial deformation of fasteners. The proposed methodology further elucidates the mechanism underlying post-assembly preload relaxation phenomena. Experimental validation through quasi-static testing confirms measurement consistency across torque-preload-angle parameters, with theoretical predictions showing excellent consistency with experimental data. This analytical advancement enhances fundamental understanding of bolted joint mechanics while providing theoretical guidance for engineering applications in precision assembly and structural safety assessment.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"177 ","pages":"Article 105132"},"PeriodicalIF":2.8,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143922010","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":"Physics-informed neural network for random response evaluation","authors":"Yuling Zhou ,&nbsp;Bo Tang ,&nbsp;Jie Wang,&nbsp;Deming Nie,&nbsp;Ming Xu,&nbsp;Kai Zhang","doi":"10.1016/j.ijnonlinmec.2025.105141","DOIUrl":"10.1016/j.ijnonlinmec.2025.105141","url":null,"abstract":"<div><div>In this paper, we propose a physics-informed neural network algorithm (PINN) to solve Fokker–Planck–Kolmogorov (FPK) equations for stochastic dynamical systems. The primary innovation of our approach lies in decomposing the solution of the FPK equations into two components: the probability density function (PDF) of the associated degenerate systems, derived from prior knowledge, and a modified component expressed in exponential form. This decomposition provides several advantages. First, the normalization condition as a supervisory criterion to prevent a zero solution is unnecessary, which reduces computational costs during the gradient descent iteration process, particularly in high-dimensional systems. Second, this approach accommodates uneven sample points. Third, the boundary condition is automatically satisfied. We present numerical examples to demonstrate the effectiveness of the proposed physics-informed neural networks. By utilizing 2- or 3-dimensional systems as examples, comparisons with exact solutions and results from Monte Carlo simulations show strong agreement, indicating that the physics-informed neural networks can solve the Fokker-Planck-Kolmogorov (FPK) equation with high precision. We believe this method can effectively address the FPK equation for various random dynamical systems.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"176 ","pages":"Article 105141"},"PeriodicalIF":2.8,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936382","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":"Research on dynamic characteristics of electromagnetic SD oscillator system under state feedback control","authors":"Meiqi Wang ,&nbsp;Qian Zu ,&nbsp;Ruichen Wang ,&nbsp;Chengwei Qin ,&nbsp;Pengfei Liu","doi":"10.1016/j.ijnonlinmec.2025.105103","DOIUrl":"10.1016/j.ijnonlinmec.2025.105103","url":null,"abstract":"<div><div>To enhance the robustness of the smooth and discontinuous (SD) oscillator system, an electromagnet incorporating displacement-velocity state feedback control is integrated above the oscillator. The electromagnetic interaction between the electromagnet and the oscillator facilitates accelerated system stabilization. This study investigates a novel electromagnetic SD oscillator. Initially, the steady-state amplitude-frequency and phase-frequency response characteristics are derived using the averaging method, with an analysis of how each state feedback parameter influences the amplitude-frequency curve. Utilizing Lyapunov stability theory and the Routh criterion, the stability conditions for the system's periodic solutions are established. Subsequently, the Melnikov theorem is employed to determine the necessary conditions for the onset of chaos within the system. Dynamic bifurcation analysis, maximum Lyapunov exponent (LLE) curves, and system behaviors under various parameters are examined to assess the impact of state feedback parameters on the chaotic boundary curve. On this basis, the global bifurcation characteristics of different parameters of the system are studied by using the cell mapping method, and the influence of each parameter on the number of attractors and the domain of attraction is analyzed. Finally, the displacement transmissibility is used to evaluate the vibration isolation effect of the system. The findings indicate that the electromagnetic SD oscillator exhibits superior vibration reduction capabilities, effectively mitigating chaos and bifurcation phenomena. Optimal selection of state feedback parameters enables rapid system stabilization under external excitation conditions.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"176 ","pages":"Article 105103"},"PeriodicalIF":2.8,"publicationDate":"2025-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143931454","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":"Nonlinear dynamic characteristics of carriage belt conveyors on small-radius curves","authors":"Zhuang Wang ,&nbsp;Yuan Zhang ,&nbsp;Changzheng Sun ,&nbsp;Xin Chang ,&nbsp;Chengjian Wang","doi":"10.1016/j.ijnonlinmec.2025.105139","DOIUrl":"10.1016/j.ijnonlinmec.2025.105139","url":null,"abstract":"<div><div>The carriage belt conveyor offers an innovative solution for bulk mineral transportation, demonstrating the interdisciplinary application of material handling and railway engineering technologies. In this system, the conveyor belt is supported by the carriage, which moves along rails mounted on elevated legs. As the carriage moves through curves, it is subjected to various forces, including lateral tension in the conveyor belt, gravity, centrifugal force, and wheel-rail interactions. In small-radius curves, a significant nonlinear relationship between lateral tension and curve radius challenges the stability of the system. However, existing research has not sufficiently addressed the nonlinear dynamic characteristics of carriage belt conveyors. Therefore, this paper develops a mechanical model for carriage belt conveyors on small-radius curves. Theoretical analysis results show that as the curve radius increases, the lateral tension exhibits oscillatory behavior before stabilizing. Next, the dynamics of the curved section are analyzed through numerical simulations in two scenarios: with and without the inner curve elevation angle. The results reveal that the inner curve elevation angle can affect the wheel-rail lateral interaction forces. Finally, based on the calculation and numerical simulation results, adjusting the inner curve elevation angle to 8.5° effectively resolves the issue of poor system stability during turns. The findings provide valuable insights into optimizing the design and stability of light rail-based mechanical systems.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"176 ","pages":"Article 105139"},"PeriodicalIF":2.8,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143902025","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 braking stability and wheel wear of train under different track conditions and different grinders","authors":"Yuhang Zhang ,&nbsp;Kai Zhou ,&nbsp;Jinsong Zhou ,&nbsp;Chongyi Chang ,&nbsp;Dao Gong ,&nbsp;Xiaoyu Li ,&nbsp;Yiyang Song","doi":"10.1016/j.ijnonlinmec.2025.105137","DOIUrl":"10.1016/j.ijnonlinmec.2025.105137","url":null,"abstract":"<div><div>This paper investigates the impact of wheel-rail adhesion conditions and grinder action on the stability of train braking systems and wheel wear, focusing on the phenomenon of low-speed flutter during braking. A three-body wheel-rail creep model is constructed based on the three-body contact theory, followed by the establishment of a three-body four-degree-of-freedom dynamic model of the braking system, which includes the brake block, brake disc, and wheelset. Using numerical methods, the study explores the relationship between the stability of the train brake system and wheel wear. The findings indicate that friction chatter primarily occurs during low-speed braking. While optimal wheel-rail adhesion conditions can enhance braking efficiency, they also tend to exacerbate friction chatter within the braking system. Moreover, brake system flutter induces fluctuations in wheel creepage, influencing the tangential force between the wheel and rail as well as wheel-rail wear. Although the vibration frequency of creepage remains consistent across different track conditions, the amplitude of fluctuation notably increases under low adhesion wheel-rail conditions, resulting in heightened non-uniformity of wheel wear.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"176 ","pages":"Article 105137"},"PeriodicalIF":2.8,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904526","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":"Establishment of nonlinear dynamic model and study on bifurcation characteristics of non-orthogonal misaligned face gear power split -flow transmission system","authors":"Dong Hao ,&nbsp;Li Xiaoman ,&nbsp;Zhang Dongbo ,&nbsp;Hou Xiangying ,&nbsp;Jin Guanghu ,&nbsp;Wang Changjiang","doi":"10.1016/j.ijnonlinmec.2025.105134","DOIUrl":"10.1016/j.ijnonlinmec.2025.105134","url":null,"abstract":"<div><div>Study on the effects of backlash, friction, and rotational speed on the nonlinear bifurcation characteristics of Non-Orthogonal Misaligned Face Gear Power Split-Flow Transmission System (NOMFGPSFTS), aiming to provide theoretical basis and technical guidance for improving power to weight ratio, prolonging service life, and ensuring the reliability of the power transmission mechanism of innovative helicopters, ships and automobiles. An 11 degree of freedom (DOF), bending, torsion and axis coupling nonlinear dynamic model is established by using the lumped mass method. The model uses Load Tooth Contact Analysis(LTCA) method to calculate the meshing stiffness of Non-Orthogonal Misaligned Face Gear (NOMFG), and combines the key nonlinear elements, including gear tooth surface friction, backlash, support stiffness and transmission error, to facilitate an accurate representation of the system dynamics. The system's dynamic differential equations are solved using the Runge-Kutta algorithm, and the system's nonlinear characteristics are demonstrated through time domain diagrams, Fast Fourier Transform (FFT) spectrograms, phase plane diagrams, Poincaré maps and Maximum Lyapunov Exponent diagrams. Bifurcation diagrams are used to further reveal the effects of backlash, rotational speed, and friction coefficient on the system's nonlinear behavior. The study finds that with the increase of dimensionless backlash, the system transits from periodic-1 motion to chaotic motion, and may evolve into periodic-2 motion, showing obvious nonlinear vibrations. With the increase of rotating speed, the system transits from periodic-2 motion to chaotic motion, and finally realizes periodic-1 motion. With the increase of friction coefficient, the chaotic region of the system decreases. Finally, the correctness of the theoretical model is verified by experiments, which provides a theoretical basis for the stability study of the system.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"177 ","pages":"Article 105134"},"PeriodicalIF":2.8,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143921779","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 constant quasi-zero stiffness isolator with tension springs to isolate vibrations with ultralow frequency","authors":"Feng Zhao ,&nbsp;J.C. Ji ,&nbsp;Shuqian Cao ,&nbsp;Jingyang Zheng ,&nbsp;Quantian Luo","doi":"10.1016/j.ijnonlinmec.2025.105129","DOIUrl":"10.1016/j.ijnonlinmec.2025.105129","url":null,"abstract":"<div><div>Many types of quasi-zero stiffness (QZS) isolators have been developed to isolate vibrations with low frequencies. However, isolating vibrations with ultralow frequency as low as 1 Hz is still a great challenge even in laboratory tests due to the high damping of QZS prototypes. To address this issue, a novel isolator with intrinsically light damping is proposed by configurating tension springs and oblique bars. The linear or nonlinear negative stiffness generated by the horizontal tension springs and oblique bars counteracts the linear positive stiffness of the vertical tension springs to obtain the QZS-related features including nonlinear QZS, constant positive or negative dynamic stiffness, constant QZS, and constant zero stiffness. Two QZS conditions are derived and the influence of parameters on QZS is thoroughly studied. The proposed isolator with tension springs has obvious differences from the previous isolator with compression springs in terms of QZS conditions, as well as force and stiffness expressions. Then, the displacement transmissibility is calculated by using the increment harmonic balance method and the continuous arc-length algorithm, which is verified by the classical harmonic balance method. These methods have the same prediction result. Finally, a prototype is fabricated and tested. The smoother force curves with constant QZS and the higher transmissibility amplitude can be obtained in tests compared to the previous isolator with compression springs under the same configuration parameters, which verifies the theoretical formulations of the proposed isolator with light damping. The prototype is further improved by replacing linear bearings with sliders to reduce the frictional effects. As a result, vibrations with ultralow frequencies lower than 1 Hz are successfully isolated. The proposed isolator has a wider frequency band and lower transmissibility than the previous isolator with compression springs. This study offers an effective method of decreasing the large positive stiffness to obtain constant QZS for isolating vibrations with ultralow frequency.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105129"},"PeriodicalIF":2.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143890892","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}