Pub Date : 2025-11-01Epub Date: 2025-06-11DOI: 10.1016/j.ijnonlinmec.2025.105174
A.P. Chugainova, R.R. Polekhina
The problem of admissibility of discontinuities in the solutions of a hyperbolic system of two conservation laws describing quasitransverse waves in nonlinearly elastic weakly anisotropic media is studied. The standard viscous regularization method is applied to the defining system of equations. Regularization leads to the situation where two different viscosity profiles may correspond to the discontinuity. The analysis of the linear (spectral) stability of these two profiles has shown that one of them is stable while the other is unstable. This conclusion demonstrates that the definition of admissibility of a discontinuity should include the requirement of stability of the discontinuity structure (the viscosity profile).
{"title":"Admissibility of discontinuities in the solutions of a hyperbolic 2 × 2 system of conservation laws","authors":"A.P. Chugainova, R.R. Polekhina","doi":"10.1016/j.ijnonlinmec.2025.105174","DOIUrl":"10.1016/j.ijnonlinmec.2025.105174","url":null,"abstract":"<div><div>The problem of admissibility of discontinuities in the solutions of a hyperbolic system of two conservation laws describing quasitransverse waves in nonlinearly elastic weakly anisotropic media is studied. The standard viscous regularization method is applied to the defining system of equations. Regularization leads to the situation where two different viscosity profiles may correspond to the discontinuity. The analysis of the linear (spectral) stability of these two profiles has shown that one of them is stable while the other is unstable. This conclusion demonstrates that the definition of admissibility of a discontinuity should include the requirement of stability of the discontinuity structure (the viscosity profile).</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105174"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144279232","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 : 2025-11-01Epub Date: 2025-06-11DOI: 10.1016/j.ijnonlinmec.2025.105186
Zirong Niu
Determining the probability density function (PDF) solution for nonlinear systems excited to combined Gaussian and Poisson white noise is of great significance in stochastic dynamics. However, this task becomes computationally intractable for high-dimensional systems. To address this challenge, this study employs a dimension-reduction method previously developed for analyzing system responses under Gaussian white noise. Here, the method is extended to determine the stationary responses of nonlinear systems under combined Gaussian and Poisson white noise excitations. The proposed approach utilizes the generalized Fokker-Planck-Kolmogorov (GFPK) equation to describe the evolution of the system response PDF. By integrating the unconcerned state variables in the series-form GFPK equation, a one-dimensional integro-differential equation is obtained. Then, equivalent drift coefficients are introduced for this dimension-reduced GFPK equation, whose equivalent form is still a one-dimensional forward GFPK equation. Finally, the fourth-order finite difference method (FDM) is applied to solve this dimension-reduced GFPK equation, and its stationary velocity responses are obtained. A six degree-of-freedom (DOF) coupled Duffing-van der Pol system and an 8-DOF system with nonlinear terms in the velocities are demonstrated to validate the proposed approach. Numerical results show that the proposed approach is in good agreement with the Monte Carlo simulation (MCS) results. In addition, some parameters, such as nonzero mean impulse amplitudes of the Poisson noise, are discussed in the examples.
确定高斯白噪声和泊松白噪声联合激励下非线性系统的概率密度函数解在随机动力学中具有重要意义。然而，这个任务在高维系统中变得难以计算。为了解决这一挑战，本研究采用了先前开发的用于分析高斯白噪声下系统响应的降维方法。本文将该方法推广到确定高斯白噪声和泊松白噪声联合激励下非线性系统的平稳响应。该方法利用广义Fokker-Planck-Kolmogorov （GFPK）方程来描述系统响应PDF的演化。通过对级数型GFPK方程中无关状态变量的积分，得到一维积分-微分方程。然后，对该降维GFPK方程引入等效漂移系数，其等效形式仍为一维正演GFPK方程。最后，采用四阶有限差分法（FDM）对该降维GFPK方程进行求解，得到了该方程的平稳速度响应。以六自由度耦合Duffing-van der Pol系统和速度项为非线性项的八自由度系统为例验证了该方法的有效性。数值计算结果表明，该方法与蒙特卡罗模拟（MCS）结果吻合较好。此外，还讨论了泊松噪声的非零平均脉冲幅值等参数。
{"title":"Probabilistic solution of high-dimensional nonlinear systems excited by combined Gaussian and Poisson white noise","authors":"Zirong Niu","doi":"10.1016/j.ijnonlinmec.2025.105186","DOIUrl":"10.1016/j.ijnonlinmec.2025.105186","url":null,"abstract":"<div><div>Determining the probability density function (PDF) solution for nonlinear systems excited to combined Gaussian and Poisson white noise is of great significance in stochastic dynamics. However, this task becomes computationally intractable for high-dimensional systems. To address this challenge, this study employs a dimension-reduction method previously developed for analyzing system responses under Gaussian white noise. Here, the method is extended to determine the stationary responses of nonlinear systems under combined Gaussian and Poisson white noise excitations. The proposed approach utilizes the generalized Fokker-Planck-Kolmogorov (GFPK) equation to describe the evolution of the system response PDF. By integrating the unconcerned state variables in the series-form GFPK equation, a one-dimensional integro-differential equation is obtained. Then, equivalent drift coefficients are introduced for this dimension-reduced GFPK equation, whose equivalent form is still a one-dimensional forward GFPK equation. Finally, the fourth-order finite difference method (FDM) is applied to solve this dimension-reduced GFPK equation, and its stationary velocity responses are obtained. A six degree-of-freedom (DOF) coupled Duffing-van der Pol system and an 8-DOF system with nonlinear terms in the velocities are demonstrated to validate the proposed approach. Numerical results show that the proposed approach is in good agreement with the Monte Carlo simulation (MCS) results. In addition, some parameters, such as nonzero mean impulse amplitudes of the Poisson noise, are discussed in the examples.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105186"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144470021","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 : 2025-11-01Epub Date: 2025-07-23DOI: 10.1016/j.ijnonlinmec.2025.105221
Jing-Li Fu , Xiao-Fan Sun , Yong-Xin Guo , Xiang-Wei Chen , Hui-Dong Cheng
Based on the fundamental fact that it is difficult to establish the d'Alembert Lagrange principle and dynamic equations for complex (linear and nonlinear) flexible objects, this paper systematically proposes the d'Alembert Lagrange principle and Hamiltonian principle for flexible object systems using the method of Lagrangian mechanics, and establishes the basic dynamic equations for flexible object systems. Firstly, the concept of inertial force is introduced, taking into account the elastic restoring force caused by the deformation of flexible objects. Based on the equilibrium conditions of objects, the d'Alembert principle for flexible object systems is proposed; The basic principle of flexible object systems, the d'Alembert Lagrange principle, is proposed by reusing the principle of virtual displacement. Secondly, taking the field function of a flexible object as a generalized coordinate, the partial derivatives of the vector longitude determining the position of the flexible object with respect to time and space coordinates are defined as the kinetic energy and strain energy of the system. Using the classical Lagrange relationship, the Lagrange form, Nielsen form, and Appell form of the d'Alembert Lagrange principle for flexible object systems are proposed. Thirdly, based on the expressions of kinetic energy, derivative of kinetic energy, and acceleration energy of flexible object systems, as well as the physical properties of object materials (constitutive relations), the Lagrange form, Nielsen form, and Apel form of the d'Alembert Lagrange principle for flexible object systems were proposed using classical Larrangian, Nielsen, and Appell relations. Fourthly, utilizing several forms of the d'Alembert Lagrange principle, the Euler Lagrange equation, Nielsen equation, and Appell equation for flexible dynamical systems were established. Fifthly, define the generalized momentum of flexible object systems, construct the Hamiltonian function of the system, and establish the generalized Hamiltonian equation of flexible object systems using variational methods. Sixthly, for flexible object systems with nonholonomic constraints, the Lagrange multiplier method was used to derive the Lagrange equation, Nielsen equation, and Appell equation for nonholonomic flexible object systems. Two examples of rigid flexible coupling were further designed to verify the application value of the dynamic equations of flexible object systems. The D'Alembert Lagrange principle, Hamilton principle, Lagrange equation, Nielsen equation, Appell equation, and Hamilton equation of the flexible object system proposed in this article are universal and applicable to elastic systems, plastic systems, elastoplastic systems, continuous medium systems, and flexible robot systems. Another important significance of this job is to analyze the results, theories, and problem-solving methods in Li mechanics, which are applicable to flexible object systems.
{"title":"d'Alembert Lagrange principle and dynamic equations of flexible object systems","authors":"Jing-Li Fu , Xiao-Fan Sun , Yong-Xin Guo , Xiang-Wei Chen , Hui-Dong Cheng","doi":"10.1016/j.ijnonlinmec.2025.105221","DOIUrl":"10.1016/j.ijnonlinmec.2025.105221","url":null,"abstract":"<div><div>Based on the fundamental fact that it is difficult to establish the d'Alembert Lagrange principle and dynamic equations for complex (linear and nonlinear) flexible objects, this paper systematically proposes the d'Alembert Lagrange principle and Hamiltonian principle for flexible object systems using the method of Lagrangian mechanics, and establishes the basic dynamic equations for flexible object systems. Firstly, the concept of inertial force is introduced, taking into account the elastic restoring force caused by the deformation of flexible objects. Based on the equilibrium conditions of objects, the d'Alembert principle for flexible object systems is proposed; The basic principle of flexible object systems, the d'Alembert Lagrange principle, is proposed by reusing the principle of virtual displacement. Secondly, taking the field function of a flexible object as a generalized coordinate, the partial derivatives of the vector longitude determining the position of the flexible object with respect to time and space coordinates are defined as the kinetic energy and strain energy of the system. Using the classical Lagrange relationship, the Lagrange form, Nielsen form, and Appell form of the d'Alembert Lagrange principle for flexible object systems are proposed. Thirdly, based on the expressions of kinetic energy, derivative of kinetic energy, and acceleration energy of flexible object systems, as well as the physical properties of object materials (constitutive relations), the Lagrange form, Nielsen form, and Apel form of the d'Alembert Lagrange principle for flexible object systems were proposed using classical Larrangian, Nielsen, and Appell relations. Fourthly, utilizing several forms of the d'Alembert Lagrange principle, the Euler Lagrange equation, Nielsen equation, and Appell equation for flexible dynamical systems were established. Fifthly, define the generalized momentum of flexible object systems, construct the Hamiltonian function of the system, and establish the generalized Hamiltonian equation of flexible object systems using variational methods. Sixthly, for flexible object systems with nonholonomic constraints, the Lagrange multiplier method was used to derive the Lagrange equation, Nielsen equation, and Appell equation for nonholonomic flexible object systems. Two examples of rigid flexible coupling were further designed to verify the application value of the dynamic equations of flexible object systems. The D'Alembert Lagrange principle, Hamilton principle, Lagrange equation, Nielsen equation, Appell equation, and Hamilton equation of the flexible object system proposed in this article are universal and applicable to elastic systems, plastic systems, elastoplastic systems, continuous medium systems, and flexible robot systems. Another important significance of this job is to analyze the results, theories, and problem-solving methods in Li mechanics, which are applicable to flexible object systems.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105221"},"PeriodicalIF":3.2,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144723860","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 : 2025-11-01Epub Date: 2025-07-23DOI: 10.1016/j.ijnonlinmec.2025.105208
Juan N. Virla, Franco E. Dotti, Lucas Oxarango, Lisandro M. Rojas
A novel control strategy is proposed to induce and sustain stable rotational motion in a parametric pendulum. This approach is motivated by its potential application in pendulum-based wave energy converters. The control action consists of a small torque applied to the pendulum to conveniently increase its angular velocity. This torque arises from the magnetic interaction between a permanent magnet attached to the pendulum and an externally powered coil, eliminating the need for mechanical couplings which is an advantage for practical implementations. A comprehensive model is developed to describe the coupled system, incorporating the parametric pendulum, the coil, the magnet, and the control action. The resulting mathematical formulation integrates principles of electromagnetism, classical mechanics, and nonlinear dynamics, with all parameters derived directly from the physics of the system. The model is validated through experiments conducted on a custom-built test rig and supported by numerical simulations. Both experimental and computational results demonstrate that the proposed control technique effectively achieves and maintains rotations across a wide range of forcing conditions and initial states. Furthermore, its performance is shown to be comparable to more complex strategies, such as those based on Time-Delayed Feedback, while remaining considerably simpler to implement.
{"title":"Rotation control of a parametrically forced magnetic pendulum","authors":"Juan N. Virla, Franco E. Dotti, Lucas Oxarango, Lisandro M. Rojas","doi":"10.1016/j.ijnonlinmec.2025.105208","DOIUrl":"10.1016/j.ijnonlinmec.2025.105208","url":null,"abstract":"<div><div>A novel control strategy is proposed to induce and sustain stable rotational motion in a parametric pendulum. This approach is motivated by its potential application in pendulum-based wave energy converters. The control action consists of a small torque applied to the pendulum to conveniently increase its angular velocity. This torque arises from the magnetic interaction between a permanent magnet attached to the pendulum and an externally powered coil, eliminating the need for mechanical couplings which is an advantage for practical implementations. A comprehensive model is developed to describe the coupled system, incorporating the parametric pendulum, the coil, the magnet, and the control action. The resulting mathematical formulation integrates principles of electromagnetism, classical mechanics, and nonlinear dynamics, with all parameters derived directly from the physics of the system. The model is validated through experiments conducted on a custom-built test rig and supported by numerical simulations. Both experimental and computational results demonstrate that the proposed control technique effectively achieves and maintains rotations across a wide range of forcing conditions and initial states. Furthermore, its performance is shown to be comparable to more complex strategies, such as those based on Time-Delayed Feedback, while remaining considerably simpler to implement.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105208"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144702813","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 : 2025-11-01Epub Date: 2025-06-01DOI: 10.1016/j.ijnonlinmec.2025.105176
Haiyang Song
In this paper, the Johnson-Cook constitutive model and explicit algorithm are applied to the non-linear analysis of composite structures, and the aim of this paper is to provide a new method by which the response of elastic-plastic structure subjected to impact load can be obtained. The effect of strain and strain rate on structural stress is described in the Johnson-Cook constitutive model, and the calculation methods of important parameters in the Johnson-Cook constitutive model are provided. The mathematical expressions of implicit algorithm and explicit algorithm are derived, and the comparison between these two algorithms is conducted. The results show that the explicit algorithm is more suitable for the non-linear analysis of composite structures. A composite structure which consists of solid structures, shell structures and shock absorbers is used as numerical example to demonstrate the feasibility and effectiveness of the presented approach.
{"title":"Non-linear analysis of composite structure subjected to impact load based on Johnson-Cook constitutive model","authors":"Haiyang Song","doi":"10.1016/j.ijnonlinmec.2025.105176","DOIUrl":"10.1016/j.ijnonlinmec.2025.105176","url":null,"abstract":"<div><div>In this paper, the Johnson-Cook constitutive model and explicit algorithm are applied to the non-linear analysis of composite structures, and the aim of this paper is to provide a new method by which the response of elastic-plastic structure subjected to impact load can be obtained. The effect of strain and strain rate on structural stress is described in the Johnson-Cook constitutive model, and the calculation methods of important parameters in the Johnson-Cook constitutive model are provided. The mathematical expressions of implicit algorithm and explicit algorithm are derived, and the comparison between these two algorithms is conducted. The results show that the explicit algorithm is more suitable for the non-linear analysis of composite structures. A composite structure which consists of solid structures, shell structures and shock absorbers is used as numerical example to demonstrate the feasibility and effectiveness of the presented approach.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105176"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144223477","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 : 2025-11-01Epub Date: 2025-05-23DOI: 10.1016/j.ijnonlinmec.2025.105152
Vassilis S. Kalantonis , Omiros Ragos , Angela E. Perdiou , Efstathios A. Perdios
In this study, we consider an extension of the classical restricted three-body problem in which an additional three-body interaction is incorporated and investigate the resulting periodic orbits. Specifically, we analyze the Lyapunov families of planar periodic orbits that emerge from the collinear equilibrium points, along with their vertical stability characteristics. Furthermore, we delve into the three-dimensional periodic orbits that bifurcate from these planar families, focusing on spatial bifurcations with periods that are equal to, double or triple the period of the associated Lyapunov orbits. Our findings reveal the presence of various symmetry types, such as plane–plane, axis–axis or combination of both. Our analysis has been conducted for a set of parameter values associated with binary systems of a relatively large mass ratio.
{"title":"Numerical exploration of the Lyapunov families and their spatial bifurcations in the R3BP under the presence of a three-body interaction","authors":"Vassilis S. Kalantonis , Omiros Ragos , Angela E. Perdiou , Efstathios A. Perdios","doi":"10.1016/j.ijnonlinmec.2025.105152","DOIUrl":"10.1016/j.ijnonlinmec.2025.105152","url":null,"abstract":"<div><div>In this study, we consider an extension of the classical restricted three-body problem in which an additional three-body interaction is incorporated and investigate the resulting periodic orbits. Specifically, we analyze the Lyapunov families of planar periodic orbits that emerge from the collinear equilibrium points, along with their vertical stability characteristics. Furthermore, we delve into the three-dimensional periodic orbits that bifurcate from these planar families, focusing on spatial bifurcations with periods that are equal to, double or triple the period of the associated Lyapunov orbits. Our findings reveal the presence of various symmetry types, such as plane–plane, axis–axis or combination of both. Our analysis has been conducted for a set of parameter values associated with binary systems of a relatively large mass ratio.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105152"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144190401","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}
Magnetic-levitation-based energy harvesters can exhibit both strong softening and hardening nonlinearities, enabling an extended operational bandwidth. By introducing stationary magnets at center positions and tailoring the poling directions, bistable or tristable potential profiles can be systematically realized. These multi-stable configurations facilitate large-amplitude oscillations, thereby enhancing the voltage output generated via electromechanical transduction. However, previous studies have considered each magnetic interaction configuration separately, without analyzing or comparing their energy harvesting performance based on critical system parameters, such as identifying the specific excitation conditions under which each configuration performs optimally. Furthermore, the dynamic behavior in many of these studies is assessed solely through voltage measurements, without direct quantification of oscillation amplitude. In this study, we investigate how the restoring forces induced by attractive and repulsive magnetic interactions influence the system dynamics. Theoretical analysis is conducted to characterize the restoring force behavior associated with each configuration. Finite element method (FEM) simulations are performed to model the restoring forces, and the theoretical predictions are validated through static loading experiments. Electromagnetic prototypes implementing both repulsive and attractive configurations are fabricated and experimentally tested. The results demonstrate distinct multi-stable characteristics. Specifically, under identical conditions in which all system parameters are fixed except for the poling direction of a moving sub-magnet, the repulsive configuration is more effective for energy harvesting at low acceleration levels (less than 1 g), while the attractive configuration performs better at higher acceleration levels (greater than 1 g).
{"title":"A nonlinear multi-stable electromagnetic energy harvester with segmented moving magnet configuration","authors":"Yimin Fan, Yulan Liao, Xin Yang, Mu-Qing Niu, Li-Qun Chen","doi":"10.1016/j.ijnonlinmec.2025.105203","DOIUrl":"10.1016/j.ijnonlinmec.2025.105203","url":null,"abstract":"<div><div>Magnetic-levitation-based energy harvesters can exhibit both strong softening and hardening nonlinearities, enabling an extended operational bandwidth. By introducing stationary magnets at center positions and tailoring the poling directions, bistable or tristable potential profiles can be systematically realized. These multi-stable configurations facilitate large-amplitude oscillations, thereby enhancing the voltage output generated via electromechanical transduction. However, previous studies have considered each magnetic interaction configuration separately, without analyzing or comparing their energy harvesting performance based on critical system parameters, such as identifying the specific excitation conditions under which each configuration performs optimally. Furthermore, the dynamic behavior in many of these studies is assessed solely through voltage measurements, without direct quantification of oscillation amplitude. In this study, we investigate how the restoring forces induced by attractive and repulsive magnetic interactions influence the system dynamics. Theoretical analysis is conducted to characterize the restoring force behavior associated with each configuration. Finite element method (FEM) simulations are performed to model the restoring forces, and the theoretical predictions are validated through static loading experiments. Electromagnetic prototypes implementing both repulsive and attractive configurations are fabricated and experimentally tested. The results demonstrate distinct multi-stable characteristics. Specifically, under identical conditions in which all system parameters are fixed except for the poling direction of a moving sub-magnet, the repulsive configuration is more effective for energy harvesting at low acceleration levels (less than 1 g), while the attractive configuration performs better at higher acceleration levels (greater than 1 g).</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105203"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144588828","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 : 2025-11-01Epub Date: 2025-07-23DOI: 10.1016/j.ijnonlinmec.2025.105219
Zhenglong Huang, Jiazheng Wang, Desheng Zhang, Xikun Wang
Based on the structure-wake coupling van der Pol oscillator model and the quasi-steady theory (QST), this study systematically investigates the suppression mechanisms of flow-induced vibration in elastically supported rigid cylinder with an additional nonlinear energy sink (NES). Three configurations (namely: circular cylinder, square cylinder with strong coupling, and square cylinder with weak coupling) are examined to explore the influence of key structural parameters ( = 0.01–0.1, = 0.1–1, and = 0.1–1) on the vibration responses of the system. The validity of the developed model is first verified against experimental data. A novel application of the NES is proposed for the square cylinder configuration, specifically addressing the complex interaction of vortex-induced vibration (VIV) and galloping. This modeling framework enables a comprehensive evaluation of the performance of NES in mitigating vibrations under combined excitation. For the circular cylinder, the influence of a weakly nonlinear NES on pure VIV is investigated within the reduced velocity range of , focusing on parameters such as phase difference, peak amplitude, and reduced frequency. For the square cylinder, the NES-induced suppression of vibrations in the galloping state is initially analyzed within a nonlinear framework, followed by a detailed investigation of its influence on VIV and galloping over the velocity range . The results demonstrate that the addition of a weakly nonlinear NES effectively mitigates vibrations of both the circular cylinder and square cylinder, while its effectiveness is significantly diminished in the case of strongly coupled square cylinder.
{"title":"Investigation of vibration suppression by nonlinear energy sink (NES) based on structure–wake oscillator coupled model","authors":"Zhenglong Huang, Jiazheng Wang, Desheng Zhang, Xikun Wang","doi":"10.1016/j.ijnonlinmec.2025.105219","DOIUrl":"10.1016/j.ijnonlinmec.2025.105219","url":null,"abstract":"<div><div>Based on the structure-wake coupling van der Pol oscillator model and the quasi-steady theory (QST), this study systematically investigates the suppression mechanisms of flow-induced vibration in elastically supported rigid cylinder with an additional nonlinear energy sink (NES). Three configurations (namely: circular cylinder, square cylinder with strong coupling, and square cylinder with weak coupling) are examined to explore the influence of key structural parameters (<span><math><mrow><mi>β</mi></mrow></math></span> = 0.01–0.1, <span><math><mrow><msub><mi>ξ</mi><mrow><mi>n</mi><mi>e</mi><mi>s</mi></mrow></msub></mrow></math></span> = 0.1–1, and <span><math><mrow><msub><mi>k</mi><mrow><mi>n</mi><mi>e</mi><mi>s</mi></mrow></msub></mrow></math></span> = 0.1–1) on the vibration responses of the system. The validity of the developed model is first verified against experimental data. A novel application of the NES is proposed for the square cylinder configuration, specifically addressing the complex interaction of vortex-induced vibration (VIV) and galloping. This modeling framework enables a comprehensive evaluation of the performance of NES in mitigating vibrations under combined excitation. For the circular cylinder, the influence of a weakly nonlinear NES on pure VIV is investigated within the reduced velocity range of <span><math><mrow><mn>2</mn><mo>≤</mo><msub><mrow><mspace></mspace><mi>U</mi></mrow><mi>r</mi></msub><mo>≤</mo><mn>14</mn></mrow></math></span>, focusing on parameters such as phase difference, peak amplitude, and reduced frequency. For the square cylinder, the NES-induced suppression of vibrations in the galloping state is initially analyzed within a nonlinear framework, followed by a detailed investigation of its influence on VIV and galloping over the velocity range <span><math><mrow><mn>0.2</mn><mo>≤</mo><msub><mi>U</mi><mi>m</mi></msub><mo>≤</mo><mn>1.3</mn><mspace></mspace><mi>m</mi><mo>/</mo><mi>s</mi></mrow></math></span>. The results demonstrate that the addition of a weakly nonlinear NES effectively mitigates vibrations of both the circular cylinder and square cylinder, while its effectiveness is significantly diminished in the case of strongly coupled square cylinder.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105219"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144711973","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 : 2025-11-01Epub Date: 2025-07-09DOI: 10.1016/j.ijnonlinmec.2025.105206
Yao Wang , Jiande Li , Yuan Qin , Linfeng Fan , Xiankun Liu , Yong Song , Wanxiang Han
As a critical bridge connecting material properties and dynamic behaviors of system, the viscoelastic oscillator is important in engineering practice. By embedding the variable-order fractional (VOF) constitutive model into viscoelastic oscillator, a variable-order fractional viscoelastic oscillator (VOFVO) dynamic model under impact loading is established. The methods of Laplace transform method, hybrid of block-pulse function and Taylor polynomial are used to solve the system responses of VOFVO dynamic model in time and frequency domains. The Split Hopkinson Pressure Bar (SHPB) impact experiment is conduced. Through a comparative analysis with the Constant fractional-order Kelvin-Voigt (CFKV) model and the Zhu-Wang-Tang nonlinear thermo-viscoelastic constitutive (ZWT) model, the accuracy of the VOF model is validated. The results show that the VOFVO in the high elastic stage Ⅱ has the best damping characteristics with the smallest vibration amplitude, the shortest vibration period, and the fastest vibration attenuation. In the frequency domain, the resonance peaks of VOFVO responses in the three stages appear near a frequency ratio of one. The natural frequency , damping ratio and geometric factor are negatively correlated with the VOFVO responses. The first amplitude decreases from 0.017 to 0.0005 as the system parameters increased. Compared to the damping ratio , the natural frequency has a more significant impact on the system responses. The geometric factor needs to be determined by comprehensively considering the smaller vibration amplitudes and rational structural configuration.
{"title":"Analysis of the characteristics of variable-order fractional viscoelastic oscillator under impact loading","authors":"Yao Wang , Jiande Li , Yuan Qin , Linfeng Fan , Xiankun Liu , Yong Song , Wanxiang Han","doi":"10.1016/j.ijnonlinmec.2025.105206","DOIUrl":"10.1016/j.ijnonlinmec.2025.105206","url":null,"abstract":"<div><div>As a critical bridge connecting material properties and dynamic behaviors of system, the viscoelastic oscillator is important in engineering practice. By embedding the variable-order fractional (VOF) constitutive model into viscoelastic oscillator, a variable-order fractional viscoelastic oscillator (VOFVO) dynamic model under impact loading is established. The methods of Laplace transform method, hybrid of block-pulse function and Taylor polynomial are used to solve the system responses of VOFVO dynamic model in time and frequency domains. The Split Hopkinson Pressure Bar (SHPB) impact experiment is conduced. Through a comparative analysis with the Constant fractional-order Kelvin-Voigt (CFKV) model and the Zhu-Wang-Tang nonlinear thermo-viscoelastic constitutive (ZWT) model, the accuracy of the VOF model is validated. The results show that the VOFVO in the high elastic stage Ⅱ has the best damping characteristics with the smallest vibration amplitude, the shortest vibration period, and the fastest vibration attenuation. In the frequency domain, the resonance peaks of VOFVO responses in the three stages appear near a frequency ratio of one. The natural frequency <span><math><mrow><msub><mi>w</mi><mi>n</mi></msub></mrow></math></span>, damping ratio <span><math><mrow><mi>ξ</mi></mrow></math></span> and geometric factor <span><math><mrow><mi>κ</mi></mrow></math></span> are negatively correlated with the VOFVO responses. The first amplitude decreases from 0.017 to 0.0005 as the system parameters increased. Compared to the damping ratio <span><math><mrow><mi>ξ</mi></mrow></math></span>, the natural frequency <span><math><mrow><msub><mi>w</mi><mi>n</mi></msub></mrow></math></span> has a more significant impact on the system responses. The geometric factor <span><math><mrow><mi>κ</mi></mrow></math></span> needs to be determined by comprehensively considering the smaller vibration amplitudes and rational structural configuration.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105206"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144623506","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 : 2025-11-01Epub Date: 2025-07-05DOI: 10.1016/j.ijnonlinmec.2025.105199
Giulia C. Fritis , Pavel S.Z. Paz , Grigori Chapiro
This study addresses the optimization of surfactant slug design for foam injection in porous media, focusing on applications relevant to carbon capture and storage (CCS) and carbon capture, utilization, and storage (CCUS). We describe the foam flow in a one-dimensional porous medium as a sequence of two Riemann problems, explicitly accounting for surfactant adsorption on the rock surface impacting the surfactant mass available for foam generation. Utilizing the modified implicit texture foam model from the commercial simulator CMG/STARS, we extended previous Riemann problem solutions to include more realistic modeling. Following the classical definition of optimal slug size, we propose a methodology to minimize surfactant usage while maximizing carbon dioxide storage efficiency. The resulting Pareto front offers valuable insights for practical applications. Our key findings indicate a strong dependence of optimal slug properties on adsorption parameters, underscoring the importance of accurately modeling reservoir rock surface — surfactant interactions. Despite employing the linear Henry adsorption isotherm, the identified optimal surfactant concentrations are primarily low, corresponding to the parameter range where this model is physically accurate, supporting our approach. Additionally, Pareto front analysis suggests a methodology to investigate the economic potential of the foam injection. All analytical solutions were validated through direct numerical simulations.
{"title":"Modeling the optimal foam injection slug in porous medium accounting adsorption effects","authors":"Giulia C. Fritis , Pavel S.Z. Paz , Grigori Chapiro","doi":"10.1016/j.ijnonlinmec.2025.105199","DOIUrl":"10.1016/j.ijnonlinmec.2025.105199","url":null,"abstract":"<div><div>This study addresses the optimization of surfactant slug design for foam injection in porous media, focusing on applications relevant to carbon capture and storage (CCS) and carbon capture, utilization, and storage (CCUS). We describe the foam flow in a one-dimensional porous medium as a sequence of two Riemann problems, explicitly accounting for surfactant adsorption on the rock surface impacting the surfactant mass available for foam generation. Utilizing the modified implicit texture foam model from the commercial simulator CMG/STARS, we extended previous Riemann problem solutions to include more realistic modeling. Following the classical definition of optimal slug size, we propose a methodology to minimize surfactant usage while maximizing carbon dioxide storage efficiency. The resulting Pareto front offers valuable insights for practical applications. Our key findings indicate a strong dependence of optimal slug properties on adsorption parameters, underscoring the importance of accurately modeling reservoir rock surface — surfactant interactions. Despite employing the linear Henry adsorption isotherm, the identified optimal surfactant concentrations are primarily low, corresponding to the parameter range where this model is physically accurate, supporting our approach. Additionally, Pareto front analysis suggests a methodology to investigate the economic potential of the foam injection. All analytical solutions were validated through direct numerical simulations.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"178 ","pages":"Article 105199"},"PeriodicalIF":2.8,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579950","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}
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