Pub Date : 2024-12-19DOI: 10.1016/j.ijnonlinmec.2024.104994
Mao Lin Deng, Wei Qiu Zhu, Qiang Feng Lü
Hysteretic nonlinearity is a common phenomenon in engineering fields, and many mathematical models have been developed to describe it. In theory, hysteretic restoring forces are generally decomposed into equivalent stiffness and equivalent damping. However, due to the complexity of hysteretic nonlinearity, obtaining analytical expressions for these equivalent components is extremely challenging. In terms of theoretical methods, most existing research focuses on single-degree-of-freedom (SDOF) hysteretic systems, and there are few analytical solutions for multi-degree-of-freedom (MDOF) hysteretic systems. This paper proposes a method for studying the response of stochastically excited MDOF hysteretic systems. Using the Bouc-Wen hysteretic model as an example, the expressions for the equivalent stiffness and damping coefficients are obtained. By applying the stochastic averaging method, the statistics of the system response can be obtained. An example is given to illustrate this method, and the numerical results show that this method can accurately predict the response of MDOF hysteretic systems under random excitation.
{"title":"Stationary response of MDOF hysteretic system under random excitation","authors":"Mao Lin Deng, Wei Qiu Zhu, Qiang Feng Lü","doi":"10.1016/j.ijnonlinmec.2024.104994","DOIUrl":"10.1016/j.ijnonlinmec.2024.104994","url":null,"abstract":"<div><div>Hysteretic nonlinearity is a common phenomenon in engineering fields, and many mathematical models have been developed to describe it. In theory, hysteretic restoring forces are generally decomposed into equivalent stiffness and equivalent damping. However, due to the complexity of hysteretic nonlinearity, obtaining analytical expressions for these equivalent components is extremely challenging. In terms of theoretical methods, most existing research focuses on single-degree-of-freedom (SDOF) hysteretic systems, and there are few analytical solutions for multi-degree-of-freedom (MDOF) hysteretic systems. This paper proposes a method for studying the response of stochastically excited MDOF hysteretic systems. Using the Bouc-Wen hysteretic model as an example, the expressions for the equivalent stiffness and damping coefficients are obtained. By applying the stochastic averaging method, the statistics of the system response can be obtained. An example is given to illustrate this method, and the numerical results show that this method can accurately predict the response of MDOF hysteretic systems under random excitation.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104994"},"PeriodicalIF":2.8,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136656","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}
In the paper, we report a new analytical method to solve the forced bistable Duffing oscillator with large amplitude periodic vibrations. The analytical solution is given in terms of the Jacobi elliptic function of corresponding conservative system and harmonic solution of nonconservative system. First, in order to simplify the influence of elliptic function on the subsequent calculation, we use the higher order harmonics to approximate the elliptic function solution of conservative system and find that the velocity term often has higher harmonic components than the displacement term. In addition, we demonstrate the accuracy of this phenomenon by using the amplitude spectrum. Furthermore, we combine this phenomenon with the perturbation method to solve the approximate response of a forced bistable Duffing oscillator with damping and harmonic excitation. Different system parameter values are selected for analytical verification, and the analytic results are consistent with those obtained by the fixed-step fourth-order Runge–Kutta method (RK-4), which verifies the accuracy of the analytical solution. This indicates that the proposed method is suitable for solving the forced bistable Duffing oscillator with large amplitude vibrations.
{"title":"A new analytical solution of a bistable Duffing oscillator under large amplitude periodic vibrations","authors":"Zhihang Gu , Wenan Jiang , Liqun Chen , Qinsheng Bi","doi":"10.1016/j.ijnonlinmec.2024.104969","DOIUrl":"10.1016/j.ijnonlinmec.2024.104969","url":null,"abstract":"<div><div>In the paper, we report a new analytical method to solve the forced bistable Duffing oscillator with large amplitude periodic vibrations. The analytical solution is given in terms of the Jacobi elliptic function of corresponding conservative system and harmonic solution of nonconservative system. First, in order to simplify the influence of elliptic function on the subsequent calculation, we use the higher order harmonics to approximate the elliptic function solution of conservative system and find that the velocity term often has higher harmonic components than the displacement term. In addition, we demonstrate the accuracy of this phenomenon by using the amplitude spectrum. Furthermore, we combine this phenomenon with the perturbation method to solve the approximate response of a forced bistable Duffing oscillator with damping and harmonic excitation. Different system parameter values are selected for analytical verification, and the analytic results are consistent with those obtained by the fixed-step fourth-order Runge–Kutta method (RK-4), which verifies the accuracy of the analytical solution. This indicates that the proposed method is suitable for solving the forced bistable Duffing oscillator with large amplitude vibrations.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104969"},"PeriodicalIF":2.8,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137288","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 : 2024-12-19DOI: 10.1016/j.ijnonlinmec.2024.104970
Thibaut Vadcard, Samuel Quaegebeur, Fabrice Thouverez
For the first time, the interaction between two contact nonlinearities, blade-tip/casing contact and blade/disk friction, is investigated simultaneously. This contribution addresses the associated complex coupling mechanisms on the state-of-the-art industrial fan stage ECL5/Catana open test case. Both contact interfaces are accounted for in nonlinear calculations using the harmonic balance method. First, a static analysis is performed to investigate the coupling mechanism between the friction coefficient and the static blade-tip gap. Then, the dynamics response of the blade is analyzed in forced response for two reference configurations: (1) with blade-tip/casing contacts only and (2) with blade/disk friction only. Particular attention is paid to the contact kinematics of both interfaces and the vibrational motion of the blade. The forced responses are analyzed using different local indicators of the contact interfaces. As the friction coefficient is usually uncertain, the robustness of the numerical strategy is then demonstrated by performing a large number of simulations on different root friction coefficients. In the end, even more computations are performed, as a part of sensitivity studies on first order parameters, in order to map out the different relevant quantities of both interfaces: number of contacting nodes at the tip, tip contact resultant force, energy dissipation. These large scale mappings allow to identify trends and inter-dependences between the kinematics of each interface. The originality of this paper lies in the thorough analysis of this seldom studied nonlinear interaction, that is crucially important for the design of safe and efficient aircraft engines. This work demonstrates that accounting for the blade/disk friction interface in numerical simulations strongly mitigates the dynamics of the blade-tip/casing contacts and can even prevent it for a specific range of friction coefficients.
{"title":"Numerical analysis of the coupling mechanisms between blade/disk friction and blade-tip/casing contacts on the state-of-the-art ECL5/Catana fan stage","authors":"Thibaut Vadcard, Samuel Quaegebeur, Fabrice Thouverez","doi":"10.1016/j.ijnonlinmec.2024.104970","DOIUrl":"10.1016/j.ijnonlinmec.2024.104970","url":null,"abstract":"<div><div>For the first time, the interaction between two contact nonlinearities, blade-tip/casing contact and blade/disk friction, is investigated simultaneously. This contribution addresses the associated complex coupling mechanisms on the state-of-the-art industrial fan stage ECL5/Catana open test case. Both contact interfaces are accounted for in nonlinear calculations using the harmonic balance method. First, a static analysis is performed to investigate the coupling mechanism between the friction coefficient and the static blade-tip gap. Then, the dynamics response of the blade is analyzed in forced response for two reference configurations: (1) with blade-tip/casing contacts only and (2) with blade/disk friction only. Particular attention is paid to the contact kinematics of both interfaces and the vibrational motion of the blade. The forced responses are analyzed using different local indicators of the contact interfaces. As the friction coefficient is usually uncertain, the robustness of the numerical strategy is then demonstrated by performing a large number of simulations on different root friction coefficients. In the end, even more computations are performed, as a part of sensitivity studies on first order parameters, in order to map out the different relevant quantities of both interfaces: number of contacting nodes at the tip, tip contact resultant force, energy dissipation. These large scale mappings allow to identify trends and inter-dependences between the kinematics of each interface. The originality of this paper lies in the thorough analysis of this seldom studied nonlinear interaction, that is crucially important for the design of safe and efficient aircraft engines. This work demonstrates that accounting for the blade/disk friction interface in numerical simulations strongly mitigates the dynamics of the blade-tip/casing contacts and can even prevent it for a specific range of friction coefficients.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104970"},"PeriodicalIF":2.8,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143137289","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}
Pub Date : 2024-12-17DOI: 10.1016/j.ijnonlinmec.2024.104989
K.A. Omoteso , T.O. Roy-Layinde , U.H. Diala
Inherent nonlinearities, present in dynamical systems are employed to solve various engineering problems. Nonlinear dynamics involve responses that are not directly proportional to inputs, allowing for more effective system management. The beneficial characteristics of nonlinear systems and its growing associated literature have contributed to mitigating industrial and environmental energy-related challenges. Several recommendations have been provided for increasing the efficiency of a vibration energy harvesting (VEH) system. In this study, we investigated the occurrence of vibrational resonance (VR) in a Duffing-type energy harvester with electromagnetic transduction structure. We explored the impact of system nonlinearities on the occurrence of VR and system performance. We employed both analytical and numerical approaches to show the impact of the system parameters, especially the nonlinear stiffness parameter on the response amplitude at low-frequency excitations. Furthermore, the estimated average power absorbed by the VEH system is selected as the system performance metric, which can be optimized using the system’s parameters of interest. The VEH system demonstrated an improved performance as a significant amount of energy was harvested based on the nonlinear parameters of interest. Our investigation points to a new approach for the design and optimization of electromagnetic energy harvester.
{"title":"Performance boost of an electromagnetic energy harvester using vibrational resonance","authors":"K.A. Omoteso , T.O. Roy-Layinde , U.H. Diala","doi":"10.1016/j.ijnonlinmec.2024.104989","DOIUrl":"10.1016/j.ijnonlinmec.2024.104989","url":null,"abstract":"<div><div>Inherent nonlinearities, present in dynamical systems are employed to solve various engineering problems. Nonlinear dynamics involve responses that are not directly proportional to inputs, allowing for more effective system management. The beneficial characteristics of nonlinear systems and its growing associated literature have contributed to mitigating industrial and environmental energy-related challenges. Several recommendations have been provided for increasing the efficiency of a vibration energy harvesting (VEH) system. In this study, we investigated the occurrence of vibrational resonance (VR) in a Duffing-type energy harvester with electromagnetic transduction structure. We explored the impact of system nonlinearities on the occurrence of VR and system performance. We employed both analytical and numerical approaches to show the impact of the system parameters, especially the nonlinear stiffness parameter on the response amplitude at low-frequency excitations. Furthermore, the estimated average power absorbed by the VEH system is selected as the system performance metric, which can be optimized using the system’s parameters of interest. The VEH system demonstrated an improved performance as a significant amount of energy was harvested based on the nonlinear parameters of interest. Our investigation points to a new approach for the design and optimization of electromagnetic energy harvester.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104989"},"PeriodicalIF":2.8,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136654","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}
Pub Date : 2024-12-16DOI: 10.1016/j.ijnonlinmec.2024.104990
Yanbo Cao , Ge Yan , Jiajia Lu , Wenhao Qi , Tianyu Zhao , Dianlong Yu , Longqi Cai , Yang Li , Wenming Zhang
This article delves into the vibration suppression and dynamics of a pipeline-soft clamp system, incorporating nonlinearity, through the utilization of a non-smooth nonlinear energy sink (NSNES) featuring piecewise linear stiffness, specifically targeting bending vibrations. Building upon the fact that the clamp, as a vital supporting component, introduces constrained nonlinearity and complex dynamics into the pipeline system, this paper primarily focuses on elucidating and investigating the impact of the nonlinearity inherent in soft clamps on the vibration mitigation performance of the NSNES. In this study, the finite element method is utilized to develop a dynamic model of a pipeline-soft clamp system, showcasing nonlinear stiffness and damping forces in the clamps. Following the introduction of the NSNES model, the dynamic model of the pipeline-soft clamp-NSNES system is elucidated. The vibration attenuation potential of the NSNES within the pipeline-soft clamp system is assessed through base steady-state excitation, with the optimization achieved via a genetic algorithm (GA). Subsequently, the key impact of the nonlinear properties of the soft clamp on the vibration suppression effect of NSNES is emphasized. The findings show that the soft clamp, when employed standalone, exhibits a certain degree of vibration reduction capacity to mitigate the vibration response of the pipeline. Remarkably, the inherent soft nonlinearity within the pipeline-soft clamp system does not detract from the exceptional vibration suppression performance of the NSNES. In fact, the NSNES maintains its superior vibration attenuation capabilities even within this nonlinear environment, demonstrating its robustness and adaptability in enhancing the overall stability and performance of the pipeline-soft clamp system. Under steady-state vibrations, the NSNES demonstrates a peak vibration elimination of 82.7% in simulations without clamp nonlinearity, whereas this figure drops to 72.2% when nonlinearity is introduced, owing to the decreased response of the pipeline-soft clamp system. In experimental tests, the NSNES effectively suppressed vibrations by 71.7% for the pipeline-soft clamp system.
{"title":"Vibration mitigation and dynamics of pipeline system with nonlinear soft clamp by a nonlinear energy sink","authors":"Yanbo Cao , Ge Yan , Jiajia Lu , Wenhao Qi , Tianyu Zhao , Dianlong Yu , Longqi Cai , Yang Li , Wenming Zhang","doi":"10.1016/j.ijnonlinmec.2024.104990","DOIUrl":"10.1016/j.ijnonlinmec.2024.104990","url":null,"abstract":"<div><div>This article delves into the vibration suppression and dynamics of a pipeline-soft clamp system, incorporating nonlinearity, through the utilization of a non-smooth nonlinear energy sink (NSNES) featuring piecewise linear stiffness, specifically targeting bending vibrations. Building upon the fact that the clamp, as a vital supporting component, introduces constrained nonlinearity and complex dynamics into the pipeline system, this paper primarily focuses on elucidating and investigating the impact of the nonlinearity inherent in soft clamps on the vibration mitigation performance of the NSNES. In this study, the finite element method is utilized to develop a dynamic model of a pipeline-soft clamp system, showcasing nonlinear stiffness and damping forces in the clamps. Following the introduction of the NSNES model, the dynamic model of the pipeline-soft clamp-NSNES system is elucidated. The vibration attenuation potential of the NSNES within the pipeline-soft clamp system is assessed through base steady-state excitation, with the optimization achieved via a genetic algorithm (GA). Subsequently, the key impact of the nonlinear properties of the soft clamp on the vibration suppression effect of NSNES is emphasized. The findings show that the soft clamp, when employed standalone, exhibits a certain degree of vibration reduction capacity to mitigate the vibration response of the pipeline. Remarkably, the inherent soft nonlinearity within the pipeline-soft clamp system does not detract from the exceptional vibration suppression performance of the NSNES. In fact, the NSNES maintains its superior vibration attenuation capabilities even within this nonlinear environment, demonstrating its robustness and adaptability in enhancing the overall stability and performance of the pipeline-soft clamp system. Under steady-state vibrations, the NSNES demonstrates a peak vibration elimination of 82.7% in simulations without clamp nonlinearity, whereas this figure drops to 72.2% when nonlinearity is introduced, owing to the decreased response of the pipeline-soft clamp system. In experimental tests, the NSNES effectively suppressed vibrations by 71.7% for the pipeline-soft clamp system.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104990"},"PeriodicalIF":2.8,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136655","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 : 2024-12-15DOI: 10.1016/j.ijnonlinmec.2024.104992
Gil-Yong Lee, Moonsu Park, Kwanghyun Ahn
This work presents nonlinear steady-state and stability analyses of rotor systems supported by hydrodynamic journal bearings. The rotor and fluid film are discretized using finite elements to incorporate shaft flexibility and various bearing configurations. The harmonic balance method is employed to analyze steady-state responses in the frequency domain, eliminating the need for time integration and handling both static and dynamic loads. Coupling between the rotor and fluid problems is achieved through an alternating frequency-time scheme, enabling parallelization to further improve computational efficiency. The stability of the solutions is evaluated using Floquet exponents derived from Hill's method, utilizing the by-products of the harmonic balance framework. Numerical results highlight the nonlinear effects in rotor systems with journal bearings, such as super-harmonic and resonance behaviors that cannot be captured by a linearized approach. The proposed framework provides accurate predictions of steady-state responses and stability across various conditions, while preserving computational efficiency.
{"title":"Nonlinear vibration analysis of rotor systems with hydrodynamic journal bearings using harmonic balance method","authors":"Gil-Yong Lee, Moonsu Park, Kwanghyun Ahn","doi":"10.1016/j.ijnonlinmec.2024.104992","DOIUrl":"10.1016/j.ijnonlinmec.2024.104992","url":null,"abstract":"<div><div>This work presents nonlinear steady-state and stability analyses of rotor systems supported by hydrodynamic journal bearings. The rotor and fluid film are discretized using finite elements to incorporate shaft flexibility and various bearing configurations. The harmonic balance method is employed to analyze steady-state responses in the frequency domain, eliminating the need for time integration and handling both static and dynamic loads. Coupling between the rotor and fluid problems is achieved through an alternating frequency-time scheme, enabling parallelization to further improve computational efficiency. The stability of the solutions is evaluated using Floquet exponents derived from Hill's method, utilizing the by-products of the harmonic balance framework. Numerical results highlight the nonlinear effects in rotor systems with journal bearings, such as super-harmonic and resonance behaviors that cannot be captured by a linearized approach. The proposed framework provides accurate predictions of steady-state responses and stability across various conditions, while preserving computational efficiency.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104992"},"PeriodicalIF":2.8,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136653","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}
Pub Date : 2024-12-13DOI: 10.1016/j.ijnonlinmec.2024.104985
Shubham Mehta, Meenakshi Mehra, Poonam Redhu
In real-world driving scenarios, numerous factors such as driver behavior, road conditions, weather conditions and vehicle capabilities contribute to deviations among the driver’s actual velocity and the expected velocity. These disparities can often lead to the formation of traffic congestion on a larger scale. Drivers can significantly reduce deviations and maintain smoother traffic flow by reacting properly and promptly to changing traffic conditions.
In this work, we investigate the impact of optimal velocity deviation and reaction time effect on traffic systems using lattice hydrodynamic model. The effect of these factors on traffic system stability is examined using the linear perturbation approach and finds that as reaction times increase, the vehicular flow becomes more stable according to both linear and nonlinear stability analysis. When compared to the current lattice models, the results demonstrate that the system becomes more stable when the reaction time effect and ideal velocity deviation are taken into account. We perform sensitivity analysis with respect to the parameters and , providing insights into their impact on traffic flow stability. Nonlinear analysis of the proposed model reveals jamming transitions among the freely moving phase and coexisting phase with the “kink–antikink wave” in the unstable region solution, which is the solution of the “mKdV equation”. The simulation results are consistent with the theoretical analysis of the proposed model. Our findings demonstrate that considering both optimal velocity deviation and reaction time significantly contributes to maintaining smooth traffic flow and reducing congestion, highlighting the importance of these factors in traffic modeling.
{"title":"Analysis of optimal velocity deviation with reaction time up to second order in a lattice hydrodynamic model with V2X communication","authors":"Shubham Mehta, Meenakshi Mehra, Poonam Redhu","doi":"10.1016/j.ijnonlinmec.2024.104985","DOIUrl":"10.1016/j.ijnonlinmec.2024.104985","url":null,"abstract":"<div><div>In real-world driving scenarios, numerous factors such as driver behavior, road conditions, weather conditions and vehicle capabilities contribute to deviations among the driver’s actual velocity and the expected velocity. These disparities can often lead to the formation of traffic congestion on a larger scale. Drivers can significantly reduce deviations and maintain smoother traffic flow by reacting properly and promptly to changing traffic conditions.</div><div>In this work, we investigate the impact of optimal velocity deviation and reaction time effect on traffic systems using lattice hydrodynamic model. The effect of these factors on traffic system stability is examined using the linear perturbation approach and finds that as reaction times increase, the vehicular flow becomes more stable according to both linear and nonlinear stability analysis. When compared to the current lattice models, the results demonstrate that the system becomes more stable when the reaction time effect and ideal velocity deviation are taken into account. We perform sensitivity analysis with respect to the parameters <span><math><mi>β</mi></math></span> and <span><math><msub><mrow><mi>t</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span>, providing insights into their impact on traffic flow stability. Nonlinear analysis of the proposed model reveals jamming transitions among the freely moving phase and coexisting phase with the “kink–antikink wave” in the unstable region solution, which is the solution of the “mKdV equation”. The simulation results are consistent with the theoretical analysis of the proposed model. Our findings demonstrate that considering both optimal velocity deviation and reaction time significantly contributes to maintaining smooth traffic flow and reducing congestion, highlighting the importance of these factors in traffic modeling.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104985"},"PeriodicalIF":2.8,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136652","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}
This study explores the combined effects of variable gravity and a uniform vertical throughflow on linear instability and nonlinear stability of thermal convection in a bidispersive porous medium (BDPM) characterized by relatively large macropores with single temperature field. The fluid flow in micropores and macropores is modelled using Darcy's and Brinkman's theories, respectively. The analysis encompasses three depth-dependent gravity laws: linear, quadratic, and exponential. The principle of exchange of stabilities is established. The numerically computed critical thresholds of linear instability and nonlinear stability are found to be different indicating the manifestation of subcritical instability and also the direction of throughflow dictates the stability of base flow. In particular, the upflow is found to be more stabilizing than downflow, highlighting the dominant influence of gravity variation over throughflow in determining the system's stability. Under a constant gravitational field, however, the linear instability threshold coincides precisely with the global nonlinear stability boundary in the absence of throughflow. Moreover, with throughflow, subcritical instability arises and the stability of the system remains unaffected by the direction of the throughflow.
{"title":"Throughflow and variable gravity outlooks on bidispersive porous convection with relatively large macropores","authors":"Vinit Kumar Tripathi , B.M. Shankar , I.S. Shivakumara , Amit Mahajan","doi":"10.1016/j.ijnonlinmec.2024.104976","DOIUrl":"10.1016/j.ijnonlinmec.2024.104976","url":null,"abstract":"<div><div>This study explores the combined effects of variable gravity and a uniform vertical throughflow on linear instability and nonlinear stability of thermal convection in a bidispersive porous medium (BDPM) characterized by relatively large macropores with single temperature field. The fluid flow in micropores and macropores is modelled using Darcy's and Brinkman's theories, respectively. The analysis encompasses three depth-dependent gravity laws: linear, quadratic, and exponential. The principle of exchange of stabilities is established. The numerically computed critical thresholds of linear instability and nonlinear stability are found to be different indicating the manifestation of subcritical instability and also the direction of throughflow dictates the stability of base flow. In particular, the upflow is found to be more stabilizing than downflow, highlighting the dominant influence of gravity variation over throughflow in determining the system's stability. Under a constant gravitational field, however, the linear instability threshold coincides precisely with the global nonlinear stability boundary in the absence of throughflow. Moreover, with throughflow, subcritical instability arises and the stability of the system remains unaffected by the direction of the throughflow.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104976"},"PeriodicalIF":2.8,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136651","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 : 2024-12-12DOI: 10.1016/j.ijnonlinmec.2024.104991
Yichen Wang , Jinhua Zhang , Wei Wang , Zhiyong Wang , Jun Hong , Bin Fang
In this paper, the finite contact dynamics of a linear oscillator coupled with a vibro-impact (VI) nonlinear energy sink (NES) is studied, and the influence of the finite contact stiffness on the response regime and vibration reduction performance is discussed. In this way, a two-degree-of-freedom system of a linear oscillator (LO) with the attached VI-NES based on the finite contact model is built, and the novel form of VI-NES combined piecewise and impact dynamics which is named Piecewise-Impact NES (PI-NES). The response regime and vibration reduction performance caused by the change of contact stiffness for different clearances of PI-NES are discussed. It is found that the contact stiffness will affect the internal impact numbers during an excitation period of LO, which resulting in the change of VI-NES vibration reduction and the migration of the system operating state between stable and unstable states. Further, based on the response regime evolution effect, the system under the state with poor vibration reduction can be transformed to the two symmetric impacts state with obvious amplitude suppression by adjusting the contact stiffness, so that the energy transfer and dissipation efficiency can be enhanced. Finally, the optimal analysis of stiffness and PI-NES clearance parameters is carried out, and the design criteria of system parameters under different stiffness intervals are obtained. It is found that the better vibration suppression performance will be obtained on the boundary between symmetric impacts state and SMR state under different contact stiffness.
{"title":"Research on the influence of finite contact stiffness on vibration reduction of a vibro-impact nonlinear energy sink system","authors":"Yichen Wang , Jinhua Zhang , Wei Wang , Zhiyong Wang , Jun Hong , Bin Fang","doi":"10.1016/j.ijnonlinmec.2024.104991","DOIUrl":"10.1016/j.ijnonlinmec.2024.104991","url":null,"abstract":"<div><div>In this paper, the finite contact dynamics of a linear oscillator coupled with a vibro-impact (VI) nonlinear energy sink (NES) is studied, and the influence of the finite contact stiffness on the response regime and vibration reduction performance is discussed. In this way, a two-degree-of-freedom system of a linear oscillator (LO) with the attached VI-NES based on the finite contact model is built, and the novel form of VI-NES combined piecewise and impact dynamics which is named Piecewise-Impact NES (PI-NES). The response regime and vibration reduction performance caused by the change of contact stiffness for different clearances of PI-NES are discussed. It is found that the contact stiffness will affect the internal impact numbers during an excitation period of LO, which resulting in the change of VI-NES vibration reduction and the migration of the system operating state between stable and unstable states. Further, based on the response regime evolution effect, the system under the state with poor vibration reduction can be transformed to the two symmetric impacts state with obvious amplitude suppression by adjusting the contact stiffness, so that the energy transfer and dissipation efficiency can be enhanced. Finally, the optimal analysis of stiffness and PI-NES clearance parameters is carried out, and the design criteria of system parameters under different stiffness intervals are obtained. It is found that the better vibration suppression performance will be obtained on the boundary between symmetric impacts state and SMR state under different contact stiffness.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104991"},"PeriodicalIF":2.8,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136650","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}
In this illuminating study, a new distinct family of semi-analytical solutions for the nonlinear system describing the rivulet flow of viscoplastic fluid (with the non-zero critical maximal level of plasticity τs), is presented with updating to the case of rivulet flowing on inclined heated plane surface which can be considered as the stretching plane linearly dependent on time t due to thermal expansion. Therefore, purely non-Newtonian case of solution {} of viscoplastic flow has been highlighted. It is worthnoting that the obtained unsteady solutions are fully decribed by Riccati-type ODE which means a possible jumping of rivulet flowing: sudden accelerating or decelerating of the flow at approriate moment of time. Approximate general mode for rivulet flow is obtained. Profile of pressure can be retrieved from two partial differential equations of the 1st order, depending of function τs of plasticity.
{"title":"Non-Newtonian rivulet-flows on unsteady heated plane surface","authors":"S.V. Ershkov , E.S. Baranovskii , E.Yu. Prosviryakov , A.V. Yudin","doi":"10.1016/j.ijnonlinmec.2024.104984","DOIUrl":"10.1016/j.ijnonlinmec.2024.104984","url":null,"abstract":"<div><div>In this illuminating study, a new distinct family of semi-analytical solutions for the nonlinear system describing the rivulet flow of viscoplastic fluid (with the <em>non-zero</em> critical maximal level of plasticity τ<em><sub>s</sub></em>), is presented with updating to the case of rivulet flowing on inclined <em>heated</em> plane surface which can be considered as the stretching plane linearly dependent on time <em>t</em> due to thermal expansion. Therefore, purely non-Newtonian case of solution {<span><math><mover><mi>v</mi><mo>→</mo></mover><mo>=</mo><mfenced><mrow><mspace></mspace><msub><mi>v</mi><mi>x</mi></msub><mo>,</mo><msub><mi>v</mi><mi>y</mi></msub></mrow></mfenced><mo>,</mo><mi>p</mi></math></span>} of viscoplastic flow has been highlighted. It is worthnoting that the obtained unsteady solutions are fully decribed by <em>Riccati</em>-type ODE which means a possible jumping of rivulet flowing: sudden accelerating or decelerating of the flow at approriate moment of time. Approximate general mode for rivulet flow is obtained. Profile of pressure can be retrieved from two partial differential equations of the 1st order, depending of function τ<sub><em>s</em></sub> of plasticity.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"170 ","pages":"Article 104984"},"PeriodicalIF":2.8,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143136649","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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