Pub Date : 2024-08-22DOI: 10.1016/j.ijnonlinmec.2024.104869
This paper first detects hidden system from plastic deformation of metallic glasses by sparse identification. The extracted model simulates four types of stress-time curves and displays the prediction of serrated events. This interpretation effectively explains various experimental phenomena of repeated yielding. Further, in terms of parametric sensitivity analysis to the model, two parameters are taken as bifurcation parameter, and the analysis of codimension-one and codimension-two bifurcation are carried out to excavate the causes of dynamic transformation, including saddle–node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and cusp bifurcation. Different bifurcation points correspond different types of stress-time curves. The homologous phase diagrams including periodic orbit, unstable orbit and chaotic behavior are presented to show the dynamics diversity of the model. In addition to dynamic analysis, statistical analysis for plasticity values is also applied to excavate the crossover between periodic and chaotic plastic dynamic transitions. Our results provide a novel perspective on the deformation of metallic glasses from the viewpoint of dynamic model and are also important for evaluating the plastic deformation properties of metallic glasses in practical applications.
{"title":"Extracting and analyzing the governing model for plastic deformation of metallic glasses","authors":"","doi":"10.1016/j.ijnonlinmec.2024.104869","DOIUrl":"10.1016/j.ijnonlinmec.2024.104869","url":null,"abstract":"<div><p>This paper first detects hidden system from plastic deformation of metallic glasses by sparse identification. The extracted model simulates four types of stress-time curves and displays the prediction of serrated events. This interpretation effectively explains various experimental phenomena of repeated yielding. Further, in terms of parametric sensitivity analysis to the model, two parameters are taken as bifurcation parameter, and the analysis of codimension-one and codimension-two bifurcation are carried out to excavate the causes of dynamic transformation, including saddle–node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and cusp bifurcation. Different bifurcation points correspond different types of stress-time curves. The homologous phase diagrams including periodic orbit, unstable orbit and chaotic behavior are presented to show the dynamics diversity of the model. In addition to dynamic analysis, statistical analysis for plasticity values is also applied to excavate the crossover between periodic and chaotic plastic dynamic transitions. Our results provide a novel perspective on the deformation of metallic glasses from the viewpoint of dynamic model and are also important for evaluating the plastic deformation properties of metallic glasses in practical applications.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142121950","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}
Pub Date : 2024-08-20DOI: 10.1016/j.ijnonlinmec.2024.104878
High-aspect-ratio (HAR) airplane wings have higher energy efficiency and present an economical alternative to standard airplane wings. HAR wings have a high span and a high lift-to-drag ratio, allowing the wing to require less thrust during flight. However, due to their length and construction, HAR wings exhibit low-frequency, high-amplitude vibrations in both vertical (yaw axis) and longitudinal (roll axis) directions. To combat these unwanted vibrations, a two-dimensional nonlinear vibration absorber (2D-NVA) is constructed and attached to a model HAR-wing airplane to verify its effectiveness at reducing vibrational motion. The 2D-NVA design, which was presented in a previous study, consists of two low-mass, rigid bodies namely the housing and the impactor. The housing consists of a ring-like rigid body in the shape of an ellipse, while the impactor is a solid cylindrical mass which resides inside the cavity of the housing. The 2D-NVA is designed such that the impactor can contact the inner surface of the housing under both impacts and constrained sliding motion. The present study focuses on the use of the 2D-NVA to mitigate multiple modes of vibration excited by impulsive loading of a model airplane with HAR wings in both vertical and longitudinal directions. The effectiveness of a single 2D-NVA is investigated computationally using a finite element model of the model airplane. These results are verified experimentally and the performance of two 2D-NVAs (one on each wing) is also investigated. The contributions of this work are that: 1) the 2D-NVA alters the global response of the model aircraft by mitigating all relevant modes in both directions simultaneously; 2) a single 2D-NVA is optimal for mitigating motion in the vertical direction, while two active 2D-NVAs are optimal for the longitudinal direction; and 3) the performance of the 2D-NVA is robust to changes in the frequency content of the parent structure.
高宽比(HAR)机翼具有更高的能效,是标准机翼的经济替代品。高宽比机翼具有高跨度和高升阻比,使机翼在飞行过程中需要的推力更小。然而,由于其长度和结构,HAR 机翼在垂直(偏航轴)和纵向(滚动轴)方向上都会出现低频、高振幅振动。为了消除这些不必要的振动,我们建造了一个二维非线性振动吸收器(2D-NVA),并将其安装在 HAR 机翼模型飞机上,以验证其减少振动运动的有效性。二维非线性减震器的设计已在之前的研究中介绍过,它由两个低质量的刚体组成,即外壳和冲击器。外壳由一个椭圆形的环状刚体组成,而撞击器则是一个位于外壳空腔内的实心圆柱体。2D-NVA 的设计使撞击器在撞击和受约束滑动运动时都能接触到外壳的内表面。本研究的重点是使用 2D-NVA 来减缓由带 HAR 机翼的模型飞机在垂直和纵向方向上受到冲击加载所激发的多种振动模式。使用模型飞机的有限元模型对单一 2D-NVA 的有效性进行了计算研究。实验验证了这些结果,并研究了两个 2D-NVA 的性能(每个机翼一个)。这项工作的贡献在于1)2D-NVA 通过同时减轻两个方向上的所有相关模态来改变模型飞机的整体响应;2)单个 2D-NVA 对于减轻垂直方向上的运动是最佳的,而两个主动 2D-NVA 对于纵向方向是最佳的;3)2D-NVA 的性能对于母体结构频率含量的变化是稳健的。
{"title":"Vibration mitigation of a model aircraft with high-aspect-ratio wings using two-dimensional nonlinear vibration absorbers","authors":"","doi":"10.1016/j.ijnonlinmec.2024.104878","DOIUrl":"10.1016/j.ijnonlinmec.2024.104878","url":null,"abstract":"<div><p>High-aspect-ratio (HAR) airplane wings have higher energy efficiency and present an economical alternative to standard airplane wings. HAR wings have a high span and a high lift-to-drag ratio, allowing the wing to require less thrust during flight. However, due to their length and construction, HAR wings exhibit low-frequency, high-amplitude vibrations in both vertical (yaw axis) and longitudinal (roll axis) directions. To combat these unwanted vibrations, a two-dimensional nonlinear vibration absorber (2D-NVA) is constructed and attached to a model HAR-wing airplane to verify its effectiveness at reducing vibrational motion. The 2D-NVA design, which was presented in a previous study, consists of two low-mass, rigid bodies namely the housing and the impactor. The housing consists of a ring-like rigid body in the shape of an ellipse, while the impactor is a solid cylindrical mass which resides inside the cavity of the housing. The 2D-NVA is designed such that the impactor can contact the inner surface of the housing under both impacts and constrained sliding motion. The present study focuses on the use of the 2D-NVA to mitigate multiple modes of vibration excited by impulsive loading of a model airplane with HAR wings in both vertical and longitudinal directions. The effectiveness of a single 2D-NVA is investigated computationally using a finite element model of the model airplane. These results are verified experimentally and the performance of two 2D-NVAs (one on each wing) is also investigated. The contributions of this work are that: 1) the 2D-NVA alters the global response of the model aircraft by mitigating all relevant modes in both directions simultaneously; 2) a single 2D-NVA is optimal for mitigating motion in the vertical direction, while two active 2D-NVAs are optimal for the longitudinal direction; and 3) the performance of the 2D-NVA is robust to changes in the frequency content of the parent structure.</p></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142048923","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}
Pub Date : 2024-08-20DOI: 10.1016/j.ijnonlinmec.2024.104873
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 ), Darcy number and an increase in the value of depth ratio (; 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 () in the vicinity of the bifurcation point except for . In such a situation, subcritical (supercritical) bifurcation is witnessed for (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.
本研究的重点是对各向异性的非均质多孔域(流体域的下层)中的泊伊休耶流进行有限振幅分析。通过对 Poiseuille 流施加有限振幅扰动来研究非线性相互作用。前者在模态振幅方面的相互作用决定了基模、扭曲的平均流、二次谐波和扭曲的基模。从线性理论中得到的最不稳定模态依次递增求解谐波,以确定立方朗道方程,这反过来又有助于确定分岔现象。所提出的弱非线性理论预测,在这种叠加系统中,存在向普瓦赛流湍流的亚临界过渡。一般来说,在远离分叉点时,不均匀度值(以 Ai 表示)和达西数(δ)的减小以及深度比值(dˆ;流体域厚度与多孔域厚度之比)的增大有利于亚临界分叉。对于所考虑的参数变化,除了 dˆ=0.2,Ai=1 外,无论分岔点附近介质各向异性(ξ)的值如何,分岔(亚临界或超临界)都保持不变。在这种情况下,ξ=0.001,0.01,0.1 (1,3) 时会出现亚临界(超临界)分岔。此外,与各向同性和均质多孔介质相反,当远离分叉点时,亚临界和超临界分叉都会出现。通过线性理论得出的模式类型与通过非线性理论得出的分岔类型之间存在对应关系,而二次流动模式则进一步证实了这一点。最后,与各向同性和均质多孔介质相比,所提出的理论结果表明亚临界向湍流过渡的开始时间较早。
{"title":"Instability, bifurcation and nonlinear dynamics of Poiseuille flow in fluid overlying an anisotropic and inhomogeneous porous domain","authors":"","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":null,"pages":null},"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}
Pub Date : 2024-08-19DOI: 10.1016/j.ijnonlinmec.2024.104859
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.
{"title":"Dynamics, stability and bifurcations of a planar three-link swimmer with passive visco-elastic joint using “ideal fluid” model","authors":"","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":null,"pages":null},"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}
Pub Date : 2024-08-18DOI: 10.1016/j.ijnonlinmec.2024.104875
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.
{"title":"Discrete mechanical model for nonlinear dynamical analysis of planar guyed towers considering the unilateral contact of cables","authors":"","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":null,"pages":null},"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}
Pub Date : 2024-08-16DOI: 10.1016/j.ijnonlinmec.2024.104874
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.
{"title":"Stability analysis of rolling mill system for flexible rolling process based on maximum Lyapunov exponent","authors":"","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":null,"pages":null},"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}
Pub Date : 2024-08-14DOI: 10.1016/j.ijnonlinmec.2024.104839
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 and time delay , 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 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.
本文研究了具有单延迟反馈回路的光电存储计算(RC)系统的共二维分岔和复杂动力学。我们主要关注其基础系统的霍普夫-霍普夫分岔。首先,我们应用 Matlab 中的 DDE-BIFTOOL 对两个分岔参数(即反馈强度 β 和时间延迟 τ)的分岔图进行了勾画,并发现了霍普夫-霍普夫分岔点的存在。然后,利用多尺度方法得到它们的正态形,并利用正态形方法对它们的局部动力学进行展开和分类。然后进行数值模拟来验证这些结果。我们发现了系统在特定区域的丰富动力学行为。此外,我们还在系统中发现了其他复杂的动力学现象,如快慢现象、周期 n 解和嵌合体。所有这些丰富的动力学现象都为这个具有单延迟反馈回路的光电存储计算系统提供了优异的潜在性能。
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Pub Date : 2024-08-10DOI: 10.1016/j.ijnonlinmec.2024.104867
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.
{"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":"","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":null,"pages":null},"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}
Pub Date : 2024-08-08DOI: 10.1016/j.ijnonlinmec.2024.104871
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.
{"title":"Investigation on dynamic modelling and nonlinear vibration behaviors of composite structures: A case of cable-beam model","authors":"","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":null,"pages":null},"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}
Pub Date : 2024-08-08DOI: 10.1016/j.ijnonlinmec.2024.104868
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.
{"title":"Using differential-algebraic equations and natural coordinates for modelling and simulating cable-driven parallel robots","authors":"","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":null,"pages":null},"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}