International Journal of Non-Linear Mechanics最新文献

{"title":"Instability, bifurcation and nonlinear dynamics of Poiseuille flow in fluid overlying an anisotropic and inhomogeneous porous domain","authors":"A. Aleria,&nbsp;P. Bera","doi":"10.1016/j.ijnonlinmec.2024.104873","DOIUrl":"10.1016/j.ijnonlinmec.2024.104873","url":null,"abstract":"<div><p>The present study focuses on the finite amplitude analysis of Poiseuille flow in an anisotropic and inhomogeneous porous domain that underlies a fluid domain. The nonlinear interactions are studied by imposing finite amplitude disturbances to the Poiseuille flow. The former interactions in terms of modal amplitudes dictate the fundamental mode, the distorted mean flow, the second harmonic and the distorted fundamental mode. The harmonics are solved progressively in increasing order of the least stable mode obtained from the linear theory to ascertain the cubic Landau equation, which in turn helps to determine the bifurcation phenomena. The presented weakly nonlinear theory predicts the existence of subcritical transition to turbulence of Poiseuille flow in such superposed systems. In general, on moving away from the bifurcation point, it is found that a decrease in the value of inhomogeneity (in terms of <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>), Darcy number <span><math><mrow><mo>(</mo><mi>δ</mi><mo>)</mo></mrow></math></span> and an increase in the value of depth ratio (<span><math><mover><mrow><mi>d</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>; the ratio of fluid domain thickness to that of porous domain) favours subcritical bifurcation. For the considered variation of parameters, the bifurcation, either subcritical or supercritical, remains the same irrespective of the value of media anisotropy (<span><math><mi>ξ</mi></math></span>) in the vicinity of the bifurcation point except for <span><math><mrow><mover><mrow><mi>d</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>=</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>,</mo><msub><mrow><mi>A</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mn>1</mn></mrow></math></span>. In such a situation, subcritical (supercritical) bifurcation is witnessed for <span><math><mrow><mi>ξ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>1</mn></mrow></math></span> (1,3). Furthermore, in contrast to isotropic and homogeneous porous media, both subcritical and supercritical bifurcations are observed when moving away from the bifurcation point. A correspondence between the type of mode via linear theory and the type of bifurcation via nonlinear theory is witnessed, which is further affirmed by the secondary flow patterns. Finally, the presented theoretical results reveal an early onset of subcritical transition to turbulence in comparison with isotropic and homogeneous porous media.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104873"},"PeriodicalIF":2.8,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142048925","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":"Dynamics, stability and bifurcations of a planar three-link swimmer with passive visco-elastic joint using “ideal fluid” model","authors":"Elon Tovi,&nbsp;Anna Zigelman,&nbsp;Yizhar Or","doi":"10.1016/j.ijnonlinmec.2024.104859","DOIUrl":"10.1016/j.ijnonlinmec.2024.104859","url":null,"abstract":"<div><p>Articulated swimming robots have a promising potential for various marine applications. A common theoretical model assumes ideal fluid, where the viscosity is negligible and the swimmer–fluid interaction is induced by reactive forces originating from added mass effect. Some previous works used this model to study planar multi-link swimmers under kinematic input prescribing all joint angles. Inspired by biological swimmers in nature that utilize body flexibility, in this work we consider an underactuated three-link swimmer where one joint is periodically actuated while the other joint is passive and viscoelastic. Analysis of the swimmer’s nonlinear dynamics reveals that its motion depends significantly on the amplitude and frequency of the actuated joint angle. Optimal frequency is found where the swimmer’s net displacement per cycle is maximized, under symmetric periodic oscillations of the passive joint. In addition, upon crossing critical values of amplitude or frequency, the system undergoes a bifurcation where the symmetric periodic solution loses stability and asymmetric solutions evolve, for which the swimmer moves along an arc. We analyze these phenomena using numerical simulations and analytical methods of perturbation expansion, harmonic balance, Floquet theory, and Hill’s determinant. The results demonstrate the important role of parametric excitation in stability and bifurcations of motion for flexible underactuated locomotion.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104859"},"PeriodicalIF":2.8,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142012709","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":"Discrete mechanical model for nonlinear dynamical analysis of planar guyed towers considering the unilateral contact of cables","authors":"Fernanda N. Silva,&nbsp;Frederico M.A. Silva","doi":"10.1016/j.ijnonlinmec.2024.104875","DOIUrl":"10.1016/j.ijnonlinmec.2024.104875","url":null,"abstract":"<div><p>Towers are widely used for power line transmission, wind power plants, TV and radio broadcasting, and telecommunications. To enhance their stability, cables are often employed to anchor these towers to the ground. In this study, we investigate the nonlinear static and dynamic responses of a planar guyed tower in which the unilateral constraints on the cables are considered. A representative discrete mechanical model with two degrees of freedom is developed to simulate the central mast of the tower, and the cables are modeled as unilateral springs with linear stiffness. The nonlinear equilibrium equations are derived using an energy approach that incorporates the dissipative forces, total potential, and kinetic energies into the Euler-Lagrange equations. Unilateral cable contact is directly included in the nonlinear equilibrium equation for the guyed tower, allowing for numerical analysis without the need to evaluate the contact point at each time or load step. Several numerical strategies are employed to obtain nonlinear static equilibrium paths, bifurcation diagrams, phase portraits, and Poincaré sections. Our analyses provide novel results for the influence of unilateral cable contact in nonlinear static and dynamic analysis, evaluating the effects of unilateral contact and prestressing on the results. A parametric analysis reveals that cable contact affects nonlinear oscillations, bifurcation, and stability. Our numerical results indicate that unilateral cable contact introduces less structural stiffness compared to bilateral contact, thereby significantly affecting the static and dynamic stability of a planar guyed tower. This is evidenced by a decrease in the static limit load and alterations in the bifurcation diagrams, where unilateral contact destroys the trivial solutions, leading to periodic and quasi-periodic solutions at low levels of vertical load.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104875"},"PeriodicalIF":2.8,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142041060","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":"Stability analysis of rolling mill system for flexible rolling process based on maximum Lyapunov exponent","authors":"Jin Wang ,&nbsp;Xiangyang Zhao ,&nbsp;Eugenio Brusa ,&nbsp;Cristiana Delprete ,&nbsp;Xinxiang Hou ,&nbsp;Xiaoli Xiang ,&nbsp;Chen Wang ,&nbsp;Yan Peng","doi":"10.1016/j.ijnonlinmec.2024.104874","DOIUrl":"10.1016/j.ijnonlinmec.2024.104874","url":null,"abstract":"<div><p>Flexible rolling technology is the current development trend of strip production industry. However, due to the simultaneous change of mechanical, process and strip specification parameters in the flexible rolling process, the motion state of the system is difficult to analyze and stability control is hard to achieve. In this paper, the active motion characteristics of rolls in flexible rolling technology are considered, and the dynamic rolling process model is established to reflect the influence mechanism of process and specification parameters on the dynamic rolling force. The dynamic model of a 4-high rolling mill was developed and the structure-process-strip coupling strategy was applied to couple the models. The Runge-Kutta method was applied to solve the dynamic equation to obtain the maximum Lyapunov exponential spectrum for a single parameter variation. It is noteworthy that the two-parameter dynamics method was adopted to solve the dynamics on the two-parameter plane considering the nature of simultaneous variation of the system parameters, which solves the limitations of the traditional analytical method and is suitable for the application of the flexible rolling system. The results suggest that the parameters influence the motion state in the form of coupling, the influence pattern of each parameter on the stability is clarified, the evolution of the stable domain under the effect of parameter coupling is revealed, and the parameter matching strategy is determined. The results will provide a solution for the system parameter setting of flexible rolling technology and a theoretical reference for enhancing the stability of the rolling mill.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"166 ","pages":"Article 104874"},"PeriodicalIF":2.8,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142011867","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":"Hopf-Hopf bifurcation, period n solutions, slow-fast phenomena, and chimera of an optoelectronic reservoir computing system with single delayed feedback loop","authors":"Lijun Pei,&nbsp;Muhammad Aiyaz","doi":"10.1016/j.ijnonlinmec.2024.104839","DOIUrl":"10.1016/j.ijnonlinmec.2024.104839","url":null,"abstract":"<div><p>In this paper, we investigate the co-dimension two bifurcations and complicated dynamics of an optoelectronic reservoir computing (RC) system with single delayed feedback loop. We focuses primarily on its underlying system’s Hopf-Hopf bifurcation. Firstly, we apply DDE-BIFTOOL built in Matlab to sketch the bifurcation diagrams with respect to two bifurcation parameters, namely feedback strength <span><math><mrow><mi>β</mi></mrow></math></span> and time delay <span><math><mrow><mi>τ</mi></mrow></math></span>, and find the existence of the Hopf-Hopf bifurcation points. Then, using the multiple scales method, we obtain their normal forms, and using the normal form method, we unfold and classify their local dynamics. Then numerical simulations are conducted to verify these results. We discover rich dynamical behaviors of the system in specific regions. Besides, other complicated dynamics, such as fast-slow phenomena, Period <span><math><mrow><mi>n</mi></mrow></math></span> solutions, and chimera, are found in the system. All these rich dynamical phenomena can provide excellent performance potentially for this optoelectronic reservoir computing system with single delayed feedback loop.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104839"},"PeriodicalIF":2.8,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142048924","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":"Novel approach for precise identification of vibration frequencies and damping ratios from free vibration decay time histories data of nonlinear single degree of freedom models","authors":"Fernando M.A. Nogueira,&nbsp;Flávio S. Barbosa","doi":"10.1016/j.ijnonlinmec.2024.104867","DOIUrl":"10.1016/j.ijnonlinmec.2024.104867","url":null,"abstract":"<div><p>The significance of Single Degree of Freedom (SDOF) systems lies in their ability to serve as foundational elements for modeling more complex dynamic problems. By capturing essential dynamic behavior with simplicity, SDOF models enable efficient analysis and comprehension of complex systems, justifying the investigation of these simplified models. In nonlinear scenarios, SDOF models result in time series data wherein vibration frequencies vary over time. Classically, time–frequency or Hilbert transforms applied to temporal responses are frequently used to identify the evolution of frequencies and damping ratio over time. These techniques provide results that reflect the spectrum composition achieved for the analyzed time window and present difficulties in precisely determining the magnitude and the exact instant of an effective frequency or damping ratio variation. In this sense, this work introduces a new methodology capable of accurately identifying the vibration frequency as a function of time, i.e., the instantaneous frequency, along with the instantaneous damping ratio. At this initial stage, the focus is on validating the methodology by comparing its performance with the classical approach based on time–frequency transforms. The initial results obtained from synthetic free vibration decay responses of SDOF nonlinear models highlight the accuracy of our findings compared to those obtained from time–frequency transforms. The presented methodology holds promise for further advancement, with potential impacts including structural damage identification, modal identification and nonlinear dynamic analysis.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104867"},"PeriodicalIF":2.8,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141992740","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 modelling and nonlinear vibration behaviors of composite structures: A case of cable-beam model","authors":"Houjun Kang ,&nbsp;Siyi Meng ,&nbsp;Yunyue Cong ,&nbsp;Tieding Guo ,&nbsp;Xiaoyang Su","doi":"10.1016/j.ijnonlinmec.2024.104871","DOIUrl":"10.1016/j.ijnonlinmec.2024.104871","url":null,"abstract":"<div><p>This paper conducts a nonlinear analysis of cable-beam model of cable-stayed bridges by using the exact mode superposition method (EMSM) and the cable-beam dragging method (CBDM), respectively, comparing and exploring their theoretical foundations and practical implications. The EMSM is based on the global mode function of the cable-beam structure for nonlinear analysis, yet it requires more computational resources. The CBDM is based on the cable-beam dragging equations for nonlinear analysis, which can quickly obtain the static equilibrium state and dynamic response of the cable-beam system, but it requires some simplifying assumptions on the cable-beam connection conditions. Research results demonstrate qualitative and quantitative differences between these two methods through parametric analysis on dynamic behaviors, which provide a significant methodological study and a reference for the design and dynamics of composite structures.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"166 ","pages":"Article 104871"},"PeriodicalIF":2.8,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141979003","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":"Using differential-algebraic equations and natural coordinates for modelling and simulating cable-driven parallel robots","authors":"Giulio Piva,&nbsp;Dario Richiedei,&nbsp;Alberto Trevisani","doi":"10.1016/j.ijnonlinmec.2024.104868","DOIUrl":"10.1016/j.ijnonlinmec.2024.104868","url":null,"abstract":"<div><p>This paper proposes a comprehensive approach to the dynamic modelling of Cable-Driven Parallel Robots (CDPRs) by means of Differential-Algebraic Equations (DAEs). CDPRs are usually modelled through a minimal set of Ordinary Differential Equations (ODEs), often by making some simplification or just focusing on the unconstrained platform/end-effector dynamics. The alternative use of redundant DAEs provides several benefits since several non-ideal properties and peculiar operations of CDPRs can be easily and accurately modelled. To provide a comprehensive modelling frame, the typical components of a CDPR with rigid cables are here discussed and modelled by exploiting the concept of DAEs, which use redundant coordinates and embed kinematic constraints in the algebraic part of the equations. Through such advantageous features, it is possible to model swivelling guiding pulleys with non-negligible dimensions and mass. The use of rheonomous constraints is proposed as well, to represent in a simple way the effect of the movable exit-points, that are widely adopted in reconfigurable CDPRs. Finally, the use of Natural Coordinates is proposed for representing spatial end-effectors and modelling some challenging operations such as its overturning or the picking of heavy objects. Numerical simulations and the comparison with the results provided by a benchmark software are shown to demonstrate the accuracy and the computational efficiency of the proposed approach.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104868"},"PeriodicalIF":2.8,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020746224002336/pdfft?md5=e943ac2797ee8f3b5c103835a2b6acba&pid=1-s2.0-S0020746224002336-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142098920","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":"Transition from planar to 3D motion in a model of nonlinear liquid sloshing","authors":"Y. Hoffman ,&nbsp;O. Katsir ,&nbsp;U. Tamir ,&nbsp;E. Shimshi ,&nbsp;O.V. Gendelman","doi":"10.1016/j.ijnonlinmec.2024.104872","DOIUrl":"10.1016/j.ijnonlinmec.2024.104872","url":null,"abstract":"<div><p>A transition from two-dimensional to three-dimensional liquid sloshing in a symmetric vessel under external periodic forcing is considered. The three-dimensional response is commonly associated with well-ordered swirling, although can exhibit also a chaotic behaviour. Such transition is well-known in the vicinity of the primary 1:1 resonance between the lowest eigenfrequency of the sloshing mass, and the frequency of the external force. The transition pattern, i.e., the dependence of the transition threshold on amplitude and frequency of the external forcing, demonstrates remarkable qualitative similarity for very different physical settings. This observation is illustrated by comparing the results of our own experiments concerning the sloshing in relatively soft cylindrical shell, to earlier results with rigid tanks of different geometry. The aforementioned similarity allows one to assume that this transition can be described by means of low-order phenomenological dynamical model with universal general structure. The parameters of such model should depend on the specific physical setting of the sloshing system. The suggested model comprises a two-dimensional damped nonlinear oscillator with unidirectional forcing. The transition to the swirling in the original sloshing system is associated with the loss of stability of the one-dimensional response in the reduced model. Analysis by means of a multiple-scale expansion allows mapping the transition threshold on the plane of parameters for given initial conditions. One reveals that in order to match the available numeric and experimental results; a polynomial model with combined softening and hardening is required. The results are verified by means of direct numeric simulations of the complete reduced-order model; additional response patterns are revealed.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104872"},"PeriodicalIF":2.8,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141978845","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 path integration method for the stochastic soft-impact systems","authors":"Liang Wang,&nbsp;Yu Wen,&nbsp;Jiahui Peng,&nbsp;Zhonghua Zhang,&nbsp;Wei Xu","doi":"10.1016/j.ijnonlinmec.2024.104866","DOIUrl":"10.1016/j.ijnonlinmec.2024.104866","url":null,"abstract":"<div><p>This paper presents an improved path integration method for a soft-impact system under stochastic excitation, which focuses on the response of the system on the impact surface. The system involves complex impact processes, including contact, deformation, recovery, and disengagement. To address the technical challenges posed by the system discontinuity at the moment of impact, we establish a mapping relation between impact events to solve the system response. Considering that the non-smooth moment of such systems exists only at the moment of contact with the impact surface, we chose to select the impact surface as a Poincaré cross-section. Two independent mappings were established to describe the transition of the oscillator from leaving the obstacle to the next contact with the obstacle, and from contacting the obstacle to leaving the obstacle. These two consecutive mappings were integrated into the plane to form a unified mapping. This method was employed to investigate the response probability density function of the system for autonomous and non-autonomous systems, respectively. The effectiveness of the methodology was validated by the use of Monte Carlo simulations, in addition to the discovery of the stochastic P-bifurcation phenomenon.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"167 ","pages":"Article 104866"},"PeriodicalIF":2.8,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141978846","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}