International Journal of Non-Linear Mechanics最新文献

{"title":"A constant quasi-zero stiffness isolator with tension springs to isolate vibrations with ultralow frequency","authors":"Feng Zhao ,&nbsp;J.C. Ji ,&nbsp;Shuqian Cao ,&nbsp;Jingyang Zheng ,&nbsp;Quantian Luo","doi":"10.1016/j.ijnonlinmec.2025.105129","DOIUrl":"10.1016/j.ijnonlinmec.2025.105129","url":null,"abstract":"<div><div>Many types of quasi-zero stiffness (QZS) isolators have been developed to isolate vibrations with low frequencies. However, isolating vibrations with ultralow frequency as low as 1 Hz is still a great challenge even in laboratory tests due to the high damping of QZS prototypes. To address this issue, a novel isolator with intrinsically light damping is proposed by configurating tension springs and oblique bars. The linear or nonlinear negative stiffness generated by the horizontal tension springs and oblique bars counteracts the linear positive stiffness of the vertical tension springs to obtain the QZS-related features including nonlinear QZS, constant positive or negative dynamic stiffness, constant QZS, and constant zero stiffness. Two QZS conditions are derived and the influence of parameters on QZS is thoroughly studied. The proposed isolator with tension springs has obvious differences from the previous isolator with compression springs in terms of QZS conditions, as well as force and stiffness expressions. Then, the displacement transmissibility is calculated by using the increment harmonic balance method and the continuous arc-length algorithm, which is verified by the classical harmonic balance method. These methods have the same prediction result. Finally, a prototype is fabricated and tested. The smoother force curves with constant QZS and the higher transmissibility amplitude can be obtained in tests compared to the previous isolator with compression springs under the same configuration parameters, which verifies the theoretical formulations of the proposed isolator with light damping. The prototype is further improved by replacing linear bearings with sliders to reduce the frictional effects. As a result, vibrations with ultralow frequencies lower than 1 Hz are successfully isolated. The proposed isolator has a wider frequency band and lower transmissibility than the previous isolator with compression springs. This study offers an effective method of decreasing the large positive stiffness to obtain constant QZS for isolating vibrations with ultralow frequency.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105129"},"PeriodicalIF":2.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143890892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prismatic bifurcation of electro-mechanically loaded stacked di-electric cylinders","authors":"Sanjeet Patra,&nbsp;Soham Roychowdhury","doi":"10.1016/j.ijnonlinmec.2025.105119","DOIUrl":"10.1016/j.ijnonlinmec.2025.105119","url":null,"abstract":"<div><div>Study on prismatic bifurcation of two layered stacked di-electric cylinder subjected to electro-mechanical loading has been performed. The stacked cylinders were subjected to uniform pressure at the inner surface of the inner cylinder, coupled with electric loading across the thickness of the cylinder. The cylinders were assumed to have identical material properties, and were considered to be homogeneous and isotropic solid described using the neo-Hookean model. Both axially free tube and axially stretched tube are considered for this analysis. The onset of prismatic diffuse modes for the cylinders was computed by employing linearized incremental equations on the equilibrium configurations of the stacked cylinders, which ultimately yields coupled first order linear differential equations. The effects of cylinder’s thickness on the critical voltage for triggering second mode of prismatic bifurcation was analyzed. The electrical actuation on either of the stacked cylinder results distinct prismatic bifurcation patterns from the same geometry. It was observed that the stacked cylinders may enter diffuse states before the Hessian based stability criteria fails. Moreover, it was found that a cylinder with higher total thickness cylinders requires higher critical voltage to trigger the prismatic bifurcation. The effect of internal pressure on the magnitude of critical voltage was found to be negligible. For the of axially free tube with higher pressurization, the cylinder undergoes snap-through transition instead of prismatic bifurcation.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105119"},"PeriodicalIF":2.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flip bifurcation and gait energetics of a bipedal walker with asymmetric leg movements powered by nonlinear pulse thrust","authors":"Bo Jiang ,&nbsp;Tengfei Long ,&nbsp;Qihuai Liu ,&nbsp;Guirong Jiang","doi":"10.1016/j.ijnonlinmec.2025.105120","DOIUrl":"10.1016/j.ijnonlinmec.2025.105120","url":null,"abstract":"<div><div>This article presents a walking bipedal model with asymmetric leg movements through a four-phase gait planning, represented as a nonlinear impulsive hybrid system. To achieve forward movement of the bipedal walker on the horizontal surface, we introduce a nonlinear pulse thrust in relation to the walking state at the heel strike to push the supporting leg off. By linearizing the continuous dynamics, a Poincaré map with explicit form is obtained analytically. The conditions for the stability of the period-1 gait are determined, the bifurcation of the periodic orbits is investigated, and then the gait energetics are analyzed. The theoretical analysis and numerical results show that with the change of the parameters of the pulse thrust, the biped walking exhibits the dynamic behaviors of a flip bifurcation path to chaos and generates a period-2 gait. Within the parameter range of the period-1 gait, a slight increase in the pulse thrust can significantly reduce the energy input of other parts of the bipedal system. It indicates that a well-designed pulse thrust can improve the energy efficiency of the desired periodic gait.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105120"},"PeriodicalIF":2.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coupled thermo-electric-magnetic-elastic strongly nonlinear energy harvesting and dynamic analysis from multi-source excitations","authors":"Huirong Zhang ,&nbsp;Shengxi Zhou","doi":"10.1016/j.ijnonlinmec.2025.105131","DOIUrl":"10.1016/j.ijnonlinmec.2025.105131","url":null,"abstract":"<div><div>Energy harvesting technology application scenarios have been broadened to multi-source excitations, including thermal, magnetic, and vibration, but the coupled multi-field effect makes the system response more complicated. In this paper, to analyze the response of the coupled multi-field system, theoretical modeling of the coupled thermo-electric-magnetic-elastic strongly nonlinear energy harvesting system is constructed. Correspondingly, the modified Green's function method and harmonic balance method are deployed to determine the solutions of the coupled multi-field model. The derived closed-form solutions are verified. From the theoretical analysis, we get a conclusion that the triggered thermal stresses within the structure owing to the temperature gradient are simultaneously canceled out, which is the reason why thermal excitation is not considered in the coupled force equation. This study reveals the amplitude-dependent property of temperature distribution induced by magnetically induced interwell and intrawell oscillations, i.e., coupled temperature distribution. For a strongly nonlinear beam-type energy harvesting system, results indicate that the multi-solution area is determined by excitation amplitude, frequency, and structure parameters, which means that the closed-form solutions of interwell and intrawell oscillations do not exist simultaneously. To improve the power generation performance, it is important for the energy harvesting design to intentionally operate in high power generation regions. This study provides a fundamental understanding and reference framework for coupled thermo-electric-magnetic-elastic investigation and potential application.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105131"},"PeriodicalIF":2.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear oscillators coupled by magnetic fields generated by electric coils connected in series and their applications in vibrations suppression and energy harvesting","authors":"Dariusz Grzelczyk ,&nbsp;Mateusz Wojna ,&nbsp;Ewelina Ogińska ,&nbsp;Jan Awrejcewicz ,&nbsp;Grzegorz Wasilewski ,&nbsp;Nimra Saeed","doi":"10.1016/j.ijnonlinmec.2025.105135","DOIUrl":"10.1016/j.ijnonlinmec.2025.105135","url":null,"abstract":"<div><div>In this paper an unique configuration of two nonlinear magneto-electro-mechanical oscillators coupled by magnetic fields produced by their electric coils connected in series is investigated in terms of numerical simulation and experimental analysis. The model of interaction between a permanent magnet and a single-layer electric coil existing in the literature is successfully adapted and applied to the interaction between magnet and multi-layer coil. Numerical analysis of coupled oscillators by using time histories, phase portraits and frequency characteristics is preceded by detailed mathematical modelling, identification and the study of the dynamics of the single oscillator. The identification of the key parameters of the system and experimental verification of the obtained simulation results are carried out based on the constructed experimental stand. It contains aerostatic supports allowing exact and axial guidance of the oscillators in linear motion without dry friction. A good agreement between numerical simulation and experimental data is achieved and illustrated, especially in terms of the values and shapes of the generated electromotive force and electrical power, which cannot be predicted in a simple way on the basis of empirical models. Eventually, some aspects of the investigated system in terms of vibrations suppression and energy harvesting are also considered and discussed.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105135"},"PeriodicalIF":2.8,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A phase-field fracture model for 3D film–substrate systems","authors":"San Kim ,&nbsp;Jaemin Kim","doi":"10.1016/j.ijnonlinmec.2025.105126","DOIUrl":"10.1016/j.ijnonlinmec.2025.105126","url":null,"abstract":"<div><div>Thin films bonded to substrates are widely used in various engineering applications, including microelectromechanical systems (MEMS), integrated circuits (ICs) packaging, flexible electronics and thermal barriers. Understanding the fracture behavior of film–substrate systems is critical, as complex fracture patterns often emerge due to the differing material properties between the film and substrate. This work is the first to present a unified phase-field fracture formulation that captures damage in both the film and substrate by integrating surface mechanics (Gurtin–Murdoch theory) and bulk mechanics within a thermodynamically consistent framework. Unlike previous studies that neglect substrate damage or rely on computationally intensive 3D film modeling, our approach enables efficient simulation with distinct damage evolution across material interfaces. This study proposes a novel phase-field fracture model to capture the damage evolution in film–substrate composites, where the film is treated as a two-dimensional membrane bonded to a three-dimensional substrate. Leveraging the surface mechanics in Gurtin–Murdoch theory, the model treats the film as a zero-thickness membrane with surface parameters distinct from the substrate. This approach significantly reduces computational costs compared to traditional methods that require fine 3D meshing for thin films. The finite element implementation employs a thermodynamically-consistent framework and a staggered solution scheme to solve the nonlinear governing equations, allowing for efficient simulation of coupling phase-field damage and large deformation. Two numerical examples are provided to validate the model and explore fracture behavior: (i) a 3D edge-cracked plate subjected to uniaxial tension, and (ii) an indentation test of a tough film-coated substrate. Results demonstrate distinct damage progression in the film and substrate, highlighting the role of the film in predicting the fracture. This study not only contributes to the theoretical understanding of film–substrate fracture but also paves the computational approach for future work on complex multi-layered systems and multi-physics fracture modeling.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105126"},"PeriodicalIF":2.8,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On influence of channel geometry on evaporative convection at nonlinear distribution of surface tension of evaporating liquid","authors":"Irina V. Stepanova","doi":"10.1016/j.ijnonlinmec.2025.105121","DOIUrl":"10.1016/j.ijnonlinmec.2025.105121","url":null,"abstract":"<div><div>The characteristics of the joint flow of a two-component evaporative liquid and gas–vapor mixture in a narrow channel are under study. A two-sided mathematical model based on the equations of incompressible fluid flow is used for the analysis. The constructed exact solution is applied to investigate the influence of the thicknesses of lower layer on the flow characteristics. It is assumed that the surface tension of the evaporating liquid is a linear function of temperature and a quadratic function of the concentration of the evaporating component. Such a distribution of surface tension is inherent in ethanol-aqueous solutions.</div><div>The thickness of the liquid layer at which the mass rate of evaporation is maximized is determined. The distribution of temperature and concentration fields in the working segment is discussed. Changes in the lower layer thickness, where the mass rate of evaporation is maximal, are revealed for variations in the initial concentration of the liquid mixture. Issues related to choice of length of working area are addressed. Verification of the exact solution and the assumptions under which it is constructed is performed through a comparative analysis with experimental data.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105121"},"PeriodicalIF":2.8,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analyzing the impact of nearby information of vehicles on a car-following model in a V2X communication with passing","authors":"Raveena Dangi,&nbsp;Poonam Redhu","doi":"10.1016/j.ijnonlinmec.2025.105113","DOIUrl":"10.1016/j.ijnonlinmec.2025.105113","url":null,"abstract":"<div><div>The paper introduces a revised “Car-following model” that integrates together influence of the driver’s memory and passing under V2X (vehicle to everything) environment on the traffic flow system by utilizing the “full velocity difference model” as a basis. Stability conditions are determined via linear stability analysis. The nonlinear analysis yields the “modified Korteweg–de Vries” equation in unstable regions because this equation characterizes traffic dynamics in the proximity of critical points. Results prove that the extended model improves traffic stability. In the V2X environment, information about the group of vehicles ahead and the driver’s inseption plays a major part in real-life traffic systems. The stability is enhanced if the driver gets informed about the apt velocity of more vehicles uphead and keeps it in mind. It has been noted that when drivers pay appropriate attention to the passing behavior of vehicles with memory, the unstable region diminishes under a connected vehicular system. Furthermore, numerical results corroborate theoretical findings, demonstrating the model’s effectiveness in enhancing vehicle efficiency, alleviating congestion and enhancing road safety. Implementing the enhanced model as active safety technology could mitigate collision accidents and reduce travel time with lower energy consumption.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105113"},"PeriodicalIF":2.8,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of a nonlinear aeroelastic system with parametric uncertainties under dynamic stall condition","authors":"Sourabh kumar ,&nbsp;Dheeraj Tripathi ,&nbsp;J. Venkatramani ,&nbsp;Ankit Gupta","doi":"10.1016/j.ijnonlinmec.2025.105116","DOIUrl":"10.1016/j.ijnonlinmec.2025.105116","url":null,"abstract":"<div><div>In this study, we analyse the response characteristics of a pitch-plunge aeroelastic system subjected to dynamic stall under the influence of system parametric uncertainty. These uncertainties can be caused by a lack of understanding of the system’s parameters, modelling assumptions or system-specific noise. The accuracy and safety of the structure would be enhanced by a systematic assessment of these uncertainties and their impact on the system. In order to account for this, the inflow speed (<span><math><mi>U</mi></math></span>), plunge to pitch frequency ratio (<span><math><mover><mrow><mi>ω</mi></mrow><mo>¯</mo></mover></math></span>), pitch(<span><math><msub><mrow><mi>ζ</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>), and plunge (<span><math><msub><mrow><mi>ζ</mi></mrow><mrow><mi>ξ</mi></mrow></msub></math></span>) damping ratio are all assumed to be uncertain parameters in the present nonlinear aeroelastic system. The uncertain system parameters fluctuations are modelled using a Karhunen–Loeve Expansion formulation and the aerodynamic loads at high angles-of-attacks during stall flutter are calculated using the Leishman–Beddoes (LB) semi-empirical dynamic stall model. Next, the response dynamics of the system under stall flutter conditions, are systematically investigated under isolated cases of deterministic, uncertainties in system parameters and stochastic input flow conditions. First, we investigate the effects of uncertain parameters individually and collectively on system response and then investigate response dynamics due to the effects of uncertain parameters combined with stochastic input flow for different time scales. In order to investigate the effect of system uncertainties on system and stall flutter bifurcation behaviour, stochastic phenomenological bifurcation analysis, is performed by examining the joint probability density function of the response quantities. Shannon entropy measure is used to capture the bifurcation boundary involving a topological change in the j-pdf. It is demonstrated that a phenomenologically rich class of stochastic responses, such as burst type intermittency, on-off intermittency, random oscillations, etc., are observed that give rise to complex cyclic stresses and can be critical to structural health. Importantly, we examine the occurrence of stall flutter events under parametric uncertainty, and fluctuating flow conditions and compare it with deterministic conditions. Finally, the associated fatigue damage is systematically investigated under uncertain parameters and fluctuating oncoming flow conditions.</div></div>","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105116"},"PeriodicalIF":2.8,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effect of oblique horizontal magnetic field on convection rolls","authors":"Snehashish Sarkar ,&nbsp;Sutapa Mandal ,&nbsp;Pinaki Pal","doi":"10.1016/j.ijnonlinmec.2025.105111","DOIUrl":"10.1016/j.ijnonlinmec.2025.105111","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We investigate the effect of external horizontal magnetic field applied on the convection rolls obliquely (at an angle &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; with the &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-axis) in electrically conducting low Prandtl number fluids under the paradigm of the Rayleigh–Bénard convection by performing three-dimensional direct numerical simulations. The control parameters, namely, the Chandrasekhar number (&lt;span&gt;&lt;math&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;) and the reduced Rayleigh number &lt;span&gt;&lt;math&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; (ratio of Rayleigh number to critical Rayleigh number), are varied in the ranges &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;1000&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;mn&gt;20&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for the Prandtl numbers &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Pr&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and 0.2 by considering three horizontal aspect ratios (&lt;span&gt;&lt;math&gt;&lt;mi&gt;Γ&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;): &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/math&gt;&lt;/span&gt;, 1 and 2. In the absence of the magnetic field, the convection starts in the form of steady rolls including the one parallel to the &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-axis. As the oblique horizontal magnetic field is switched on at an angle &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∘&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with the &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-axis, it is observed that the Lorentz force generated by the component of the magnetic field transverse to the axis of the convection rolls inhibits convection. Thus, with the application of the magnetic field, the convection is suppressed and restarts for a higher Rayleigh number in the form of steady convection rolls. The rolls can be oriented at angles 0° (steady parallel rolls, SPR) or 45° (steady oblique rolls, SOR&lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;) or 135° (steady oblique rolls, SOR&lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;) with the &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-axis depending on the choices of the parameters. A rich bifurcation structure consisting of standing and traveling flow patterns associated with these steady flow patterns for higher values &lt;span&gt;&lt;math&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is investigated in detail. The oscillatory instability of the steady rolls is found to scale as &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; with two distinct exponents, one each for weaker and stronger magnetic fields. The investigation reveals that for a given set of values of &lt;span&gt;&lt;math&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;Pr&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, the heat transfer is inhibited with the increase of &lt;span&gt;&lt;ma","PeriodicalId":50303,"journal":{"name":"International Journal of Non-Linear Mechanics","volume":"175 ","pages":"Article 105111"},"PeriodicalIF":2.8,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873350","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}