International Journal of Non-Linear Mechanics最新文献

{"title":"Koopman–Hill stability computation of periodic orbits in polynomial dynamical systems using a real-valued quadratic harmonic balance formulation","authors":"Fabia Bayer ,&nbsp;Remco I. Leine ,&nbsp;Olivier Thomas ,&nbsp;Aurélien Grolet","doi":"10.1016/j.ijnonlinmec.2024.104894","DOIUrl":"10.1016/j.ijnonlinmec.2024.104894","url":null,"abstract":"<div><p>In this paper, we generalize the Koopman–Hill projection method, which was recently introduced for the numerical stability analysis of periodic solutions, to be included immediately in classical real-valued harmonic balance (HBM) formulations. We incorporate it into the Asymptotic Numerical Method (ANM) continuation framework, providing a numerically efficient stability analysis tool for frequency response curves obtained through HBM. The Hill matrix, which carries stability information and follows as a by-product of the HBM solution procedure, is often computationally challenging to analyze with traditional methods. To address this issue, we generalize the Koopman–Hill projection stability method, which extracts the monodromy matrix from the Hill matrix using a matrix exponential, from complex-valued to real-valued formulations. In addition, we propose a differential recast procedure, which makes this real-valued Hill matrix immediately available within the ANM continuation framework. Using as an example a nonlinear von Kármán beam, we demonstrate that these modifications improve computational efficiency in the stability analysis of frequency response curves.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104894"},"PeriodicalIF":2.8,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020746224002592/pdfft?md5=cc371eb9d58aadca32cce4e7eedc4d4b&pid=1-s2.0-S0020746224002592-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142239734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prescribed performance control guaranteeing anti-lock braking for nonlinear uncertain electro-booster","authors":"Bangji Zhang ,&nbsp;Jiaojiao Liu ,&nbsp;Liujie Li ,&nbsp;Zheshuo Zhang","doi":"10.1016/j.ijnonlinmec.2024.104899","DOIUrl":"10.1016/j.ijnonlinmec.2024.104899","url":null,"abstract":"<div><p>Control of electro-booster is crucial for vehicle safety. Traffic accidents occur due to unmanageable control errors in the electro-booster system and tire lock-up caused by excessive braking force. Achieving consistent prescribed performance and anti-lock braking presents a challenge due to the system nonlinearity and time-varying uncertainties. In this context, this study introduces a constrained prescribed performance control (CPPC) approach for the electro-booster. We formulate the prescribed performance and the anti-lock braking as constraints of control error and input, respectively. A diffeomorphism approach is proposed to establish a mapping between an unconstrained system and the electro-booster system with constraints. No linearization are invoked in the control design and no extra anti-braking system is needed. Experiments and simulations have demonstrated that the desired braking actions can be accurately executed under uncertainties, while guaranteeing both prescribed performance and anti-lock braking.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104899"},"PeriodicalIF":2.8,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142230379","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":"Effect of relative phase of loose tie rods on nonlinear dynamic behavior of rod-fastening rotor-bearing-seal system","authors":"Xianglin Wu,&nbsp;Xiaohui Gu","doi":"10.1016/j.ijnonlinmec.2024.104888","DOIUrl":"10.1016/j.ijnonlinmec.2024.104888","url":null,"abstract":"<div><p>Loosening of multiple tie rods in a circumferential rod-fastening rotor caused by thermal deformation and centrifugal loads is very common in engineering. The relative position of loose tie rods in the circumferential direction will also have an important impact on rotor dynamics. The relevant research has not been done yet. In this paper, a contact model of the rough machined surface is firstly established by combining the probability functions describing rough surfaces and fractal contact theory of asperities, then the contact stiffness model between disks is established based on the contact model. Finally, the dynamic model of the circumferential rod-fastening rotor-bearing-seal system is established and solved. The effect of relative phase of loose tie rods on the nonlinear dynamic characteristics of rod-fastening rotor-bearing-sealing system is studied. It can be concluded that relative phase of the loose tie rod has an important influence on the frequency, bifurcation, and periodic motion of the rotor system. At lower speed, the anisotropy of contact stiffness caused by loose tie rods has little effect on the rotor trajectory, while the generalized bending moment has a greater influence on dynamics of the system. At higher speed, the anisotropy of contact stiffness has a great influence on the axis rail of the rod-fastening rotor.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104888"},"PeriodicalIF":2.8,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142161851","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":"Modeling of micromorphic continuum based on a heterogeneous microscale","authors":"Pamela D.N. Reges,&nbsp;Roque L.S. Pitangueira,&nbsp;Leandro L. Silva","doi":"10.1016/j.ijnonlinmec.2024.104881","DOIUrl":"10.1016/j.ijnonlinmec.2024.104881","url":null,"abstract":"<div><p>Generalized continuum theories have emerged as a promising solution for the limitations of traditional continuum mechanics in fully describing the behavior of materials in which the influence of the microstructure is not negligible. The macroscopic response of quasi-brittle material, for example, is closely tied to its heterogeneous microstructure and the simplifying hypothesis of classical theory is insufficient to address all the phenomena involved. By incorporating a length scale associated to the microscale, generalized continua can handle localization issues in quasi-brittle materials represented as elastic-degrading media. An important drawback that greatly limits the applicability of such generalized models is the definition of the numerous elastic parameters. Taking into account the micromorphic theory, 18 constants are required for the description of an isotropic medium. In this paper, a numerical approach for determining the micromorphic constitutive relations, previously applied only for a homogeneous medium, is detailed based on the homogenization of a heterogeneous microscale. The microstructure formed by aggregates and matrix considered in the finer-scale is generated by the take-and-place algorithm and its behavior is described by a classical continuum. An analysis is here conducted in order to understand the effect of different characteristics of the finer-scale, as mesh, microcontinuum size, and heterogeneity distribution, on the resulting macroscopic micromorphic constitutive relations. Afterwards, a simulation is presented wherein the localization phenomenon is detected and a damage model specifically proposed for the micromorphic continuum is employed. This work could lead to models that are able to capture the microstructure influence, often disregarded when modeling quasi-brittle media, within the framework of generalized continuum theory, while also addressing the challenge of defining the elastic parameters.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104881"},"PeriodicalIF":2.8,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136328","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":"Indentation of a stiff membrane on an incompressible elastic halfspace","authors":"M. Ciavarella ,&nbsp;J.R. Barber","doi":"10.1016/j.ijnonlinmec.2024.104886","DOIUrl":"10.1016/j.ijnonlinmec.2024.104886","url":null,"abstract":"<div><p>Indentation of a very stiff membrane (like graphene) on an incompressible elastic material has been suggested as a method to measure the elastic modulus of the membrane, but so far the method is less explored than that based on indentation of a free-standing membrane clamped on the outer boundary, which relies on analytical solutions. However, we analyse the problem rigorously with an energy minimization in the Rayleigh sense with a one term approximation of the vertical displacement, and show that in the fully non-linear regime, the load <span><math><mi>F</mi></math></span> has a single term solution increasing as the power 5/3 of the indentation <span><math><mi>Δ</mi></math></span>. The solution is corrected only in the prefactor by extensive FEM investigation using a concentrated load resulting finally in <span><math><mrow><mi>F</mi><mo>=</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>45</mn><mo>×</mo><mn>4</mn><mi>π</mi></mrow><mrow><msup><mrow><mfenced><mrow><mn>384</mn><mi>π</mi></mrow></mfenced></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></mfrac><msubsup><mrow><mi>μ</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></msubsup><msubsup><mrow><mi>E</mi></mrow><mrow><mi>m</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msubsup><msup><mrow><mi>Δ</mi></mrow><mrow><mn>5</mn><mo>/</mo><mn>3</mn></mrow></msup><msup><mrow><mi>h</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn></mrow></msup></mrow></math></span>, where <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> is the substrate shear modulus, <span><math><mi>h</mi></math></span> the membrane thickness, and <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> its elastic modulus. We also find the effect of a finite membrane outer radius analytically, so that this method is also based entirely on analytical solutions. Comparison with experimental results seems very promising.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104886"},"PeriodicalIF":2.8,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020746224002518/pdfft?md5=0a86cdb514503e261f5e104685d836f2&pid=1-s2.0-S0020746224002518-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142161852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Linear stability analysis of the viscoelastic Navier–Stokes–Voigt fluid model through Brinkman porous media: Modal and non-modal approaches","authors":"D.L. Shivaraj Kumar,&nbsp;M.S. Basavaraj,&nbsp;A.S. Aruna","doi":"10.1016/j.ijnonlinmec.2024.104885","DOIUrl":"10.1016/j.ijnonlinmec.2024.104885","url":null,"abstract":"<div><p>The linear stability analysis of a viscoelastic Navier-Stokes-Voigt fluid flow, or the Kelvin-Voigt fluid of zero order in a Brinkman porous medium, is investigated using both modal and non-modal analysis. The numerical solution is obtained using the Chebyshev collocation method. The combined effects of the medium's porosity, represented by the porous parameter, the fluid viscosity, represented by the ratio of effective viscosity to fluid viscosity, and the fluid elasticity, represented by the Kelvin-Voigt parameter are investigated using both modal and non-modal analysis. The modal analysis describes the long-term behavior of the system, obtained through plotting the eigenspectrum, eigenfunctions, growth rate curves, neutral stability curves, and streamline plots, along with accurate values of critical triplets. In non-modal analysis, the pseudospectrum of the Orr-Sommerfeld operator, transient energy growth curves, and regions of stability, instability, and potential instability are depicted. The results obtained from modal analysis indicate that the porous parameter, Kelvin-Voigt parameter, and the ratio of effective viscosity to fluid viscosity act as stabilizing agents. However, using non-modal analysis, it is observed that while the porous parameter and the ratio of effective viscosity to fluid viscosity act as stabilizing agents, the Kelvin-Voigt parameter acts as a destabilizing agent over shorter periods.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104885"},"PeriodicalIF":2.8,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168654","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":"Investigation on dynamic behaviors of the cage in cylindrical roller bearings based on nonlinear dynamic model with lubrication and cage whirling","authors":"Xinzhuo Zhang,&nbsp;Ruixuan Gao,&nbsp;Yongsheng Zhu,&nbsp;Qiang Tang,&nbsp;Ke Yan,&nbsp;Jun Hong","doi":"10.1016/j.ijnonlinmec.2024.104887","DOIUrl":"10.1016/j.ijnonlinmec.2024.104887","url":null,"abstract":"<div><p>The dynamic characteristics of the cages of cylindrical roller bearings (CRBs) significantly impact the service life of the bearings. This paper considers the lubrication between the roller and cage and the effect of cage whirling and establishes an accurate CRBs nonlinear dynamic model. On this basis, the correlation between the stability of the cage centroid trajectory, cage sliding characteristics, and bearing operating parameters is elaborated on. In addition, the influence of structural parameters, such as the number of rollers and pocket clearance, on the dynamic characteristics of the bearing system is also investigated. The results indicate that in the design stage of CRBs, it is essential to ensure a reasonable number of rollers and a smaller cage clearance ratio to reduce the slippage rate and enhance the stability of the bearing cage. Furthermore, during the usage stage of CRBs, changes in load or rotational speed operating parameters can lead to cage whirling. However, the stability of the cage whirling under the former condition is higher than that under the latter. Therefore, it is necessary to fully consider the reasonable rotational speed and load conditions to prevent premature damage to the cage.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104887"},"PeriodicalIF":2.8,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142128787","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":"Death transitions in attractive–repulsive coupled oscillators with higher-order interactions","authors":"Zhonghua Zhang,&nbsp;Liang Wang,&nbsp;Wei Xu","doi":"10.1016/j.ijnonlinmec.2024.104882","DOIUrl":"10.1016/j.ijnonlinmec.2024.104882","url":null,"abstract":"<div><p>The first-order phase transition from oscillation to steady state, known as explosive death (ED), is prevalent in various dynamical models. However, previous studies on ED have predominantly focused on interactions between pairs of elements. In this work, we investigate how death transitions occur when both pairwise and three-body interactions are present in an extended Van der Pol oscillator network with attractive–repulsive coupling. By examining both global and non-local interaction mechanisms, the impact of higher-order interactions on ED and the differences in the transition process are comprehensively analyzed. Firstly, we construct a diagram of the global dynamics in the context of higher-order and first-order coupling strengths, identifying that the higher-order interactions promote the onset of ED with a contribution comparable to that of first-order interactions. Specifically, for global coupling, the theoretical backward critical curves matching the numerical results are derived through linear stability analyses, showcasing a linear correlation with a slope of -1 between the higher-order and first-order coupling strengths. Under non-local coupling, fitting the numerically obtained backward critical curves likewise yields a consistent quantitative relationship. Additionally, during the transition process of ED, we discover intriguing coexisting states in the hysteresis area under non-local coupling, including the coexistence of chimera states with coherent or incoherent oscillation, and the coexistence of chimera states with oscillation death. This is attributed to symmetry breaking induced by non-local action. These findings enhance the understanding of higher-order interactions in complex systems and provide a fresh perspective for studying multi-stability behavior in biochemical and physical systems.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104882"},"PeriodicalIF":2.8,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142121949","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":"Influence of lubrication state transition on dynamic characteristics of deep groove ball bearing with localized defect in thermal environment","authors":"Xiaotian Bai ,&nbsp;Rongzheng Zou ,&nbsp;Huaitao Shi ,&nbsp;Zinan Wang ,&nbsp;Xiaochen Zhang ,&nbsp;Hao Zheng","doi":"10.1016/j.ijnonlinmec.2024.104879","DOIUrl":"10.1016/j.ijnonlinmec.2024.104879","url":null,"abstract":"<div><p>The accuracy of the vibration response in a defective bearing dynamics model depends on the precise representation of the lubrication friction state between the rolling element (RE) and the raceway within the model. In this study, a fault dynamic model for outer ring defect of deep groove ball bearings (DGBBs), considering the lubrication state transition in a thermal environment, is established. This model accounts for the asperity contact effect during the lubrication state transition and integrates the lubrication-friction model for temperature changes into the dynamic model when skidding occurs. The influence of lubrication state change on the fault frequency of outer ring of DGBB in thermal environment is studied. The experimental and simulation results indicate that the lubrication state of the bearing is gradually deteriorated from elastohydrodynamic lubrication to mixed lubrication with the increase of working temperature. The transformation of the lubrication state is shown to have a significant effect on friction, resulting in the fault frequency of the outer ring increasing with temperature, which exhibits substantial deviation in the thermal environment. In the temperature range of 30 °C–150 °C, the deviation of defect frequency reaches 15.5%, which affects the accuracy of bearing fault diagnosis. This study may offer recommendations for enhancing the condition monitoring of rolling bearings under extreme working conditions.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104879"},"PeriodicalIF":2.8,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136438","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 free vibration analysis of imperfect cylindrical panels with discontinuous unilateral elastic base","authors":"Jordana L. Morais,&nbsp;Frederico M.A. Silva","doi":"10.1016/j.ijnonlinmec.2024.104884","DOIUrl":"10.1016/j.ijnonlinmec.2024.104884","url":null,"abstract":"<div><p>In this work, the nonlinear free vibration analysis of the imperfect cylindrical panels in contact with discontinuous unilateral elastic base are conducted, evaluating the influence of the type of contact, unilateral or bilateral, and the contact area of the elastic base on the natural frequencies and nonlinear frequency-amplitude relations. For that, the structural cylindrical panel model considers the Donnell's nonlinear shallow shell theory to obtain the partial differential equilibrium equation and the compatibility and continuity equation. To represent the unilateral capability of the elastic base, a signum function is inserted in the reaction force of the elastic base to describe its dependence of the transversal displacement field of the cylindrical panel. To apply the elastic base in certain subdomain of the cylindrical panel, a Heaviside-type function is also inserted into elastic base's reaction forces. The nonlinear equilibrium equation is discretized by the Galerkin method, using a consistent transversal displacement field that it was obtained from a perturbation technique. The discretized set of equilibrium equations is employed to obtain the natural frequencies and the nonlinear frequency-amplitude relations, evaluating the influence of the unilateral contact and the contact region of the elastic base on these results. Depending on the signal of the imperfection's magnitude and the type of contact of the elastic base, the imperfect cylindrical panel can display an initial gap between the cylindrical panel and the elastic base, and this possibility is also investigated in this work. From the numerical results, it is observed that the unilateral elastic base applies less structural stiffness than the bilateral elastic base, decreasing the natural frequencies for the same imperfect cylindrical panel. The localization of the elastic base in the cylindrical panel also affects the natural frequencies, increasing or decreasing them depending on the modifications on the structural stiffness. The frequency-amplitude relations are strongly influenced by both unilateral contact of elastic base and the type of the contact consideration between the cylindrical panel and elastic base, exhibiting an intricated nonlinear behavior.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104884"},"PeriodicalIF":2.8,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142098921","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}