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Vibration mitigation of a model aircraft with high-aspect-ratio wings using two-dimensional nonlinear vibration absorbers 利用二维非线性减震器缓解高宽比机翼模型飞机的振动
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-20 DOI: 10.1016/j.ijnonlinmec.2024.104878

High-aspect-ratio (HAR) airplane wings have higher energy efficiency and present an economical alternative to standard airplane wings. HAR wings have a high span and a high lift-to-drag ratio, allowing the wing to require less thrust during flight. However, due to their length and construction, HAR wings exhibit low-frequency, high-amplitude vibrations in both vertical (yaw axis) and longitudinal (roll axis) directions. To combat these unwanted vibrations, a two-dimensional nonlinear vibration absorber (2D-NVA) is constructed and attached to a model HAR-wing airplane to verify its effectiveness at reducing vibrational motion. The 2D-NVA design, which was presented in a previous study, consists of two low-mass, rigid bodies namely the housing and the impactor. The housing consists of a ring-like rigid body in the shape of an ellipse, while the impactor is a solid cylindrical mass which resides inside the cavity of the housing. The 2D-NVA is designed such that the impactor can contact the inner surface of the housing under both impacts and constrained sliding motion. The present study focuses on the use of the 2D-NVA to mitigate multiple modes of vibration excited by impulsive loading of a model airplane with HAR wings in both vertical and longitudinal directions. The effectiveness of a single 2D-NVA is investigated computationally using a finite element model of the model airplane. These results are verified experimentally and the performance of two 2D-NVAs (one on each wing) is also investigated. The contributions of this work are that: 1) the 2D-NVA alters the global response of the model aircraft by mitigating all relevant modes in both directions simultaneously; 2) a single 2D-NVA is optimal for mitigating motion in the vertical direction, while two active 2D-NVAs are optimal for the longitudinal direction; and 3) the performance of the 2D-NVA is robust to changes in the frequency content of the parent structure.

高宽比(HAR)机翼具有更高的能效,是标准机翼的经济替代品。高宽比机翼具有高跨度和高升阻比,使机翼在飞行过程中需要的推力更小。然而,由于其长度和结构,HAR 机翼在垂直(偏航轴)和纵向(滚动轴)方向上都会出现低频、高振幅振动。为了消除这些不必要的振动,我们建造了一个二维非线性振动吸收器(2D-NVA),并将其安装在 HAR 机翼模型飞机上,以验证其减少振动运动的有效性。二维非线性减震器的设计已在之前的研究中介绍过,它由两个低质量的刚体组成,即外壳和冲击器。外壳由一个椭圆形的环状刚体组成,而撞击器则是一个位于外壳空腔内的实心圆柱体。2D-NVA 的设计使撞击器在撞击和受约束滑动运动时都能接触到外壳的内表面。本研究的重点是使用 2D-NVA 来减缓由带 HAR 机翼的模型飞机在垂直和纵向方向上受到冲击加载所激发的多种振动模式。使用模型飞机的有限元模型对单一 2D-NVA 的有效性进行了计算研究。实验验证了这些结果,并研究了两个 2D-NVA 的性能(每个机翼一个)。这项工作的贡献在于1)2D-NVA 通过同时减轻两个方向上的所有相关模态来改变模型飞机的整体响应;2)单个 2D-NVA 对于减轻垂直方向上的运动是最佳的,而两个主动 2D-NVA 对于纵向方向是最佳的;3)2D-NVA 的性能对于母体结构频率含量的变化是稳健的。
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引用次数: 0
Instability, bifurcation and nonlinear dynamics of Poiseuille flow in fluid overlying an anisotropic and inhomogeneous porous domain 各向异性和非均质多孔域上覆流体中 Poiseuille 流动的不稳定性、分岔和非线性动力学
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-20 DOI: 10.1016/j.ijnonlinmec.2024.104873

The present study focuses on the finite amplitude analysis of Poiseuille flow in an anisotropic and inhomogeneous porous domain that underlies a fluid domain. The nonlinear interactions are studied by imposing finite amplitude disturbances to the Poiseuille flow. The former interactions in terms of modal amplitudes dictate the fundamental mode, the distorted mean flow, the second harmonic and the distorted fundamental mode. The harmonics are solved progressively in increasing order of the least stable mode obtained from the linear theory to ascertain the cubic Landau equation, which in turn helps to determine the bifurcation phenomena. The presented weakly nonlinear theory predicts the existence of subcritical transition to turbulence of Poiseuille flow in such superposed systems. In general, on moving away from the bifurcation point, it is found that a decrease in the value of inhomogeneity (in terms of Ai), Darcy number (δ) and an increase in the value of depth ratio (dˆ; the ratio of fluid domain thickness to that of porous domain) favours subcritical bifurcation. For the considered variation of parameters, the bifurcation, either subcritical or supercritical, remains the same irrespective of the value of media anisotropy (ξ) in the vicinity of the bifurcation point except for dˆ=0.2,Ai=1. In such a situation, subcritical (supercritical) bifurcation is witnessed for ξ=0.001,0.01,0.1 (1,3). Furthermore, in contrast to isotropic and homogeneous porous media, both subcritical and supercritical bifurcations are observed when moving away from the bifurcation point. A correspondence between the type of mode via linear theory and the type of bifurcation via nonlinear theory is witnessed, which is further affirmed by the secondary flow patterns. Finally, the presented theoretical results reveal an early onset of subcritical transition to turbulence in comparison with isotropic and homogeneous porous media.

本研究的重点是对各向异性的非均质多孔域(流体域的下层)中的泊伊休耶流进行有限振幅分析。通过对 Poiseuille 流施加有限振幅扰动来研究非线性相互作用。前者在模态振幅方面的相互作用决定了基模、扭曲的平均流、二次谐波和扭曲的基模。从线性理论中得到的最不稳定模态依次递增求解谐波,以确定立方朗道方程,这反过来又有助于确定分岔现象。所提出的弱非线性理论预测,在这种叠加系统中,存在向普瓦赛流湍流的亚临界过渡。一般来说,在远离分叉点时,不均匀度值(以 Ai 表示)和达西数(δ)的减小以及深度比值(dˆ;流体域厚度与多孔域厚度之比)的增大有利于亚临界分叉。对于所考虑的参数变化,除了 dˆ=0.2,Ai=1 外,无论分岔点附近介质各向异性(ξ)的值如何,分岔(亚临界或超临界)都保持不变。在这种情况下,ξ=0.001,0.01,0.1 (1,3) 时会出现亚临界(超临界)分岔。此外,与各向同性和均质多孔介质相反,当远离分叉点时,亚临界和超临界分叉都会出现。通过线性理论得出的模式类型与通过非线性理论得出的分岔类型之间存在对应关系,而二次流动模式则进一步证实了这一点。最后,与各向同性和均质多孔介质相比,所提出的理论结果表明亚临界向湍流过渡的开始时间较早。
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引用次数: 0
Dynamics, stability and bifurcations of a planar three-link swimmer with passive visco-elastic joint using “ideal fluid” model 采用 "理想流体 "模型的带被动粘弹性关节的平面三连杆游泳器的动力学、稳定性和分叉问题
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-19 DOI: 10.1016/j.ijnonlinmec.2024.104859

Articulated swimming robots have a promising potential for various marine applications. A common theoretical model assumes ideal fluid, where the viscosity is negligible and the swimmer–fluid interaction is induced by reactive forces originating from added mass effect. Some previous works used this model to study planar multi-link swimmers under kinematic input prescribing all joint angles. Inspired by biological swimmers in nature that utilize body flexibility, in this work we consider an underactuated three-link swimmer where one joint is periodically actuated while the other joint is passive and viscoelastic. Analysis of the swimmer’s nonlinear dynamics reveals that its motion depends significantly on the amplitude and frequency of the actuated joint angle. Optimal frequency is found where the swimmer’s net displacement per cycle is maximized, under symmetric periodic oscillations of the passive joint. In addition, upon crossing critical values of amplitude or frequency, the system undergoes a bifurcation where the symmetric periodic solution loses stability and asymmetric solutions evolve, for which the swimmer moves along an arc. We analyze these phenomena using numerical simulations and analytical methods of perturbation expansion, harmonic balance, Floquet theory, and Hill’s determinant. The results demonstrate the important role of parametric excitation in stability and bifurcations of motion for flexible underactuated locomotion.

铰接式游泳机器人在各种海洋应用中具有广阔的发展前景。常见的理论模型假定流体是理想的,粘度可以忽略不计,游泳者与流体之间的相互作用是由质量效应产生的反作用力引起的。之前的一些研究利用该模型研究了在规定所有关节角度的运动输入条件下的平面多链节游泳者。受自然界中利用身体柔韧性的生物游泳者的启发,我们在这项研究中考虑了一种欠驱动的三连杆游泳者,其中一个关节周期性地驱动,而另一个关节则处于被动和粘弹性状态。对游泳者的非线性动力学分析表明,其运动在很大程度上取决于驱动关节角度的振幅和频率。在被动关节对称周期性摆动的情况下,可以找到泳者每个周期净位移最大的最佳频率。此外,当超过振幅或频率的临界值时,系统会发生分岔,此时对称周期解失去稳定性,而非对称解会发生演变,此时游泳者会沿着弧线移动。我们利用数值模拟以及扰动扩展、谐波平衡、Floquet 理论和希尔行列式等分析方法对这些现象进行了分析。结果证明了参数激励在柔性欠驱动运动的稳定性和运动分岔中的重要作用。
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引用次数: 0
Discrete mechanical model for nonlinear dynamical analysis of planar guyed towers considering the unilateral contact of cables 考虑缆索单侧接触的平面植被塔非线性动力学分析离散力学模型
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-18 DOI: 10.1016/j.ijnonlinmec.2024.104875

Towers are widely used for power line transmission, wind power plants, TV and radio broadcasting, and telecommunications. To enhance their stability, cables are often employed to anchor these towers to the ground. In this study, we investigate the nonlinear static and dynamic responses of a planar guyed tower in which the unilateral constraints on the cables are considered. A representative discrete mechanical model with two degrees of freedom is developed to simulate the central mast of the tower, and the cables are modeled as unilateral springs with linear stiffness. The nonlinear equilibrium equations are derived using an energy approach that incorporates the dissipative forces, total potential, and kinetic energies into the Euler-Lagrange equations. Unilateral cable contact is directly included in the nonlinear equilibrium equation for the guyed tower, allowing for numerical analysis without the need to evaluate the contact point at each time or load step. Several numerical strategies are employed to obtain nonlinear static equilibrium paths, bifurcation diagrams, phase portraits, and Poincaré sections. Our analyses provide novel results for the influence of unilateral cable contact in nonlinear static and dynamic analysis, evaluating the effects of unilateral contact and prestressing on the results. A parametric analysis reveals that cable contact affects nonlinear oscillations, bifurcation, and stability. Our numerical results indicate that unilateral cable contact introduces less structural stiffness compared to bilateral contact, thereby significantly affecting the static and dynamic stability of a planar guyed tower. This is evidenced by a decrease in the static limit load and alterations in the bifurcation diagrams, where unilateral contact destroys the trivial solutions, leading to periodic and quasi-periodic solutions at low levels of vertical load.

铁塔广泛用于输电线路、风力发电厂、电视和无线电广播以及电信。为了增强塔架的稳定性,通常采用缆索将塔架固定在地面上。在本研究中,我们研究了平面缆索塔的非线性静态和动态响应,其中考虑了缆索的单侧约束。我们建立了一个具有代表性的离散机械模型,该模型具有两个自由度,用于模拟塔的中央桅杆,并将缆索模拟为具有线性刚度的单边弹簧。非线性平衡方程采用能量法推导,将耗散力、总势能和动能纳入欧拉-拉格朗日方程。单侧缆索接触直接包含在盖梁塔架的非线性平衡方程中,因此无需在每个时间或载荷步骤评估接触点即可进行数值分析。我们采用了多种数值策略来获得非线性静态平衡路径、分岔图、相位图和 Poincaré 截面图。我们的分析提供了非线性静态和动态分析中单侧缆索接触影响的新结果,评估了单侧接触和预应力对结果的影响。参数分析表明,缆索接触会影响非线性振荡、分岔和稳定性。我们的数值结果表明,与双边接触相比,单边缆索接触引入的结构刚度较小,因此会对平面盖梁塔架的静态和动态稳定性产生显著影响。这表现在静态极限载荷的减小和分岔图的改变上,单侧接触破坏了三相解,导致在低水平垂直载荷下出现周期和准周期解。
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引用次数: 0
Stability analysis of rolling mill system for flexible rolling process based on maximum Lyapunov exponent 基于最大李雅普诺夫指数的柔性轧制工艺轧机系统稳定性分析
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-16 DOI: 10.1016/j.ijnonlinmec.2024.104874

Flexible rolling technology is the current development trend of strip production industry. However, due to the simultaneous change of mechanical, process and strip specification parameters in the flexible rolling process, the motion state of the system is difficult to analyze and stability control is hard to achieve. In this paper, the active motion characteristics of rolls in flexible rolling technology are considered, and the dynamic rolling process model is established to reflect the influence mechanism of process and specification parameters on the dynamic rolling force. The dynamic model of a 4-high rolling mill was developed and the structure-process-strip coupling strategy was applied to couple the models. The Runge-Kutta method was applied to solve the dynamic equation to obtain the maximum Lyapunov exponential spectrum for a single parameter variation. It is noteworthy that the two-parameter dynamics method was adopted to solve the dynamics on the two-parameter plane considering the nature of simultaneous variation of the system parameters, which solves the limitations of the traditional analytical method and is suitable for the application of the flexible rolling system. The results suggest that the parameters influence the motion state in the form of coupling, the influence pattern of each parameter on the stability is clarified, the evolution of the stable domain under the effect of parameter coupling is revealed, and the parameter matching strategy is determined. The results will provide a solution for the system parameter setting of flexible rolling technology and a theoretical reference for enhancing the stability of the rolling mill.

柔性轧制技术是当前板带生产行业的发展趋势。然而,由于柔性轧制过程中机械参数、工艺参数和板带规格参数同时变化,系统运动状态难以分析,稳定性控制难以实现。本文考虑了柔性轧制技术中轧辊的主动运动特性,建立了动态轧制过程模型,以反映工艺和规格参数对动态轧制力的影响机理。建立了四高轧机动态模型,并采用结构-过程-带钢耦合策略将模型耦合。采用 Runge-Kutta 方法求解动态方程,得到单参数变化的最大 Lyapunov 指数谱。值得注意的是,考虑到系统参数同时变化的特性,采用了双参数动力学方法求解双参数平面上的动力学方程,解决了传统解析法的局限性,适用于柔性滚动系统的应用。结果表明,参数以耦合形式影响运动状态,阐明了各参数对稳定性的影响规律,揭示了参数耦合作用下稳定域的演化过程,确定了参数匹配策略。研究结果将为柔性轧制技术的系统参数设置提供解决方案,为提高轧机的稳定性提供理论参考。
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引用次数: 0
Hopf-Hopf bifurcation, period n solutions, slow-fast phenomena, and chimera of an optoelectronic reservoir computing system with single delayed feedback loop 具有单延迟反馈回路的光电存储计算系统的霍普夫-霍普夫分岔、周期 n 解、慢-快现象和嵌合体
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-14 DOI: 10.1016/j.ijnonlinmec.2024.104839

In this paper, we investigate the co-dimension two bifurcations and complicated dynamics of an optoelectronic reservoir computing (RC) system with single delayed feedback loop. We focuses primarily on its underlying system’s Hopf-Hopf bifurcation. Firstly, we apply DDE-BIFTOOL built in Matlab to sketch the bifurcation diagrams with respect to two bifurcation parameters, namely feedback strength β and time delay τ, and find the existence of the Hopf-Hopf bifurcation points. Then, using the multiple scales method, we obtain their normal forms, and using the normal form method, we unfold and classify their local dynamics. Then numerical simulations are conducted to verify these results. We discover rich dynamical behaviors of the system in specific regions. Besides, other complicated dynamics, such as fast-slow phenomena, Period n solutions, and chimera, are found in the system. All these rich dynamical phenomena can provide excellent performance potentially for this optoelectronic reservoir computing system with single delayed feedback loop.

本文研究了具有单延迟反馈回路的光电存储计算(RC)系统的共二维分岔和复杂动力学。我们主要关注其基础系统的霍普夫-霍普夫分岔。首先,我们应用 Matlab 中的 DDE-BIFTOOL 对两个分岔参数(即反馈强度 β 和时间延迟 τ)的分岔图进行了勾画,并发现了霍普夫-霍普夫分岔点的存在。然后,利用多尺度方法得到它们的正态形,并利用正态形方法对它们的局部动力学进行展开和分类。然后进行数值模拟来验证这些结果。我们发现了系统在特定区域的丰富动力学行为。此外,我们还在系统中发现了其他复杂的动力学现象,如快慢现象、周期 n 解和嵌合体。所有这些丰富的动力学现象都为这个具有单延迟反馈回路的光电存储计算系统提供了优异的潜在性能。
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引用次数: 0
Novel approach for precise identification of vibration frequencies and damping ratios from free vibration decay time histories data of nonlinear single degree of freedom models 从非线性单自由度模型的自由振动衰减时间历程数据中精确识别振动频率和阻尼比的新方法
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-10 DOI: 10.1016/j.ijnonlinmec.2024.104867

The significance of Single Degree of Freedom (SDOF) systems lies in their ability to serve as foundational elements for modeling more complex dynamic problems. By capturing essential dynamic behavior with simplicity, SDOF models enable efficient analysis and comprehension of complex systems, justifying the investigation of these simplified models. In nonlinear scenarios, SDOF models result in time series data wherein vibration frequencies vary over time. Classically, time–frequency or Hilbert transforms applied to temporal responses are frequently used to identify the evolution of frequencies and damping ratio over time. These techniques provide results that reflect the spectrum composition achieved for the analyzed time window and present difficulties in precisely determining the magnitude and the exact instant of an effective frequency or damping ratio variation. In this sense, this work introduces a new methodology capable of accurately identifying the vibration frequency as a function of time, i.e., the instantaneous frequency, along with the instantaneous damping ratio. At this initial stage, the focus is on validating the methodology by comparing its performance with the classical approach based on time–frequency transforms. The initial results obtained from synthetic free vibration decay responses of SDOF nonlinear models highlight the accuracy of our findings compared to those obtained from time–frequency transforms. The presented methodology holds promise for further advancement, with potential impacts including structural damage identification, modal identification and nonlinear dynamic analysis.

单自由度(SDOF)系统的意义在于,它们能够作为更复杂动态问题建模的基础元素。通过简单地捕捉基本动态行为,SDOF 模型能够高效地分析和理解复杂系统,从而证明对这些简化模型的研究是正确的。在非线性情况下,SDOF 模型会产生振动频率随时间变化的时间序列数据。经典的时频或希尔伯特变换常用于时间响应,以确定频率和阻尼比随时间的变化。这些技术提供的结果反映了在分析时间窗口中实现的频谱组成,但难以精确确定有效频率或阻尼比变化的幅度和确切时间。从这个意义上说,这项工作引入了一种新的方法,能够准确识别振动频率与时间的函数关系,即瞬时频率和瞬时阻尼比。在初始阶段,重点是通过比较该方法与基于时频变换的经典方法的性能来验证该方法。从 SDOF 非线性模型的合成自由振动衰减响应中获得的初步结果突出表明,与通过时频变换获得的结果相比,我们的研究结果非常准确。所提出的方法有望得到进一步发展,其潜在影响包括结构损伤识别、模态识别和非线性动态分析。
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引用次数: 0
Investigation on dynamic modelling and nonlinear vibration behaviors of composite structures: A case of cable-beam model 复合材料结构的动态建模和非线性振动行为研究:以索梁模型为例
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-08 DOI: 10.1016/j.ijnonlinmec.2024.104871

This paper conducts a nonlinear analysis of cable-beam model of cable-stayed bridges by using the exact mode superposition method (EMSM) and the cable-beam dragging method (CBDM), respectively, comparing and exploring their theoretical foundations and practical implications. The EMSM is based on the global mode function of the cable-beam structure for nonlinear analysis, yet it requires more computational resources. The CBDM is based on the cable-beam dragging equations for nonlinear analysis, which can quickly obtain the static equilibrium state and dynamic response of the cable-beam system, but it requires some simplifying assumptions on the cable-beam connection conditions. Research results demonstrate qualitative and quantitative differences between these two methods through parametric analysis on dynamic behaviors, which provide a significant methodological study and a reference for the design and dynamics of composite structures.

本文分别采用精确模态叠加法(EMSM)和索梁拖曳法(CBDM)对斜拉桥的索梁模型进行了非线性分析,比较并探讨了它们的理论基础和实际意义。EMSM 基于索梁结构的全局模态函数进行非线性分析,但需要较多的计算资源。CBDM 基于索梁拖动方程进行非线性分析,可快速获得索梁系统的静态平衡状态和动态响应,但需要对索梁连接条件进行一些简化假设。研究结果通过对动态行为的参数分析,证明了这两种方法在质量和数量上的差异,为复合材料结构的设计和动力学提供了重要的方法学研究和参考。
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引用次数: 0
Using differential-algebraic equations and natural coordinates for modelling and simulating cable-driven parallel robots 利用微分代数方程和自然坐标对电缆驱动并联机器人进行建模和仿真
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-08 DOI: 10.1016/j.ijnonlinmec.2024.104868

This paper proposes a comprehensive approach to the dynamic modelling of Cable-Driven Parallel Robots (CDPRs) by means of Differential-Algebraic Equations (DAEs). CDPRs are usually modelled through a minimal set of Ordinary Differential Equations (ODEs), often by making some simplification or just focusing on the unconstrained platform/end-effector dynamics. The alternative use of redundant DAEs provides several benefits since several non-ideal properties and peculiar operations of CDPRs can be easily and accurately modelled. To provide a comprehensive modelling frame, the typical components of a CDPR with rigid cables are here discussed and modelled by exploiting the concept of DAEs, which use redundant coordinates and embed kinematic constraints in the algebraic part of the equations. Through such advantageous features, it is possible to model swivelling guiding pulleys with non-negligible dimensions and mass. The use of rheonomous constraints is proposed as well, to represent in a simple way the effect of the movable exit-points, that are widely adopted in reconfigurable CDPRs. Finally, the use of Natural Coordinates is proposed for representing spatial end-effectors and modelling some challenging operations such as its overturning or the picking of heavy objects. Numerical simulations and the comparison with the results provided by a benchmark software are shown to demonstrate the accuracy and the computational efficiency of the proposed approach.

本文提出了一种通过微分代数方程(DAE)对缆索驱动并联机器人(CDPR)进行动态建模的综合方法。CDPR 通常通过一组最小的常微分方程 (ODE) 来建模,通常会进行一些简化或仅关注无约束平台/末端执行器动态。由于可以轻松、准确地模拟 CDPR 的若干非理想特性和特殊操作,因此使用冗余 DAE 有许多好处。为了提供一个全面的建模框架,本文讨论了带刚性电缆的 CDPR 的典型组件,并利用 DAE 的概念进行建模,DAE 使用冗余坐标,并在方程的代数部分嵌入了运动学约束。利用这些优势,可以对具有不可忽略的尺寸和质量的旋转导向滑轮进行建模。我们还建议使用流变约束,以简单的方式表示可移动出口点的影响,这在可重新配置的 CDPR 中被广泛采用。最后,建议使用自然坐标来表示空间末端执行器,并模拟一些具有挑战性的操作,如翻转或拾取重物。通过数值模拟以及与基准软件提供的结果进行比较,证明了所提方法的准确性和计算效率。
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引用次数: 0
Transition from planar to 3D motion in a model of nonlinear liquid sloshing 非线性液体荡动模型中从平面运动到三维运动的过渡
IF 2.8 3区 工程技术 Q2 MECHANICS Pub Date : 2024-08-08 DOI: 10.1016/j.ijnonlinmec.2024.104872

A transition from two-dimensional to three-dimensional liquid sloshing in a symmetric vessel under external periodic forcing is considered. The three-dimensional response is commonly associated with well-ordered swirling, although can exhibit also a chaotic behaviour. Such transition is well-known in the vicinity of the primary 1:1 resonance between the lowest eigenfrequency of the sloshing mass, and the frequency of the external force. The transition pattern, i.e., the dependence of the transition threshold on amplitude and frequency of the external forcing, demonstrates remarkable qualitative similarity for very different physical settings. This observation is illustrated by comparing the results of our own experiments concerning the sloshing in relatively soft cylindrical shell, to earlier results with rigid tanks of different geometry. The aforementioned similarity allows one to assume that this transition can be described by means of low-order phenomenological dynamical model with universal general structure. The parameters of such model should depend on the specific physical setting of the sloshing system. The suggested model comprises a two-dimensional damped nonlinear oscillator with unidirectional forcing. The transition to the swirling in the original sloshing system is associated with the loss of stability of the one-dimensional response in the reduced model. Analysis by means of a multiple-scale expansion allows mapping the transition threshold on the plane of parameters for given initial conditions. One reveals that in order to match the available numeric and experimental results; a polynomial model with combined softening and hardening is required. The results are verified by means of direct numeric simulations of the complete reduced-order model; additional response patterns are revealed.

研究考虑了在外部周期性作用下,对称容器中液体从二维荡动向三维荡动的转变。三维响应通常与井然有序的漩涡有关,但也可能表现出混乱的行为。众所周知,这种转变发生在荡质的最低特征频率与外力频率之间的 1:1 主共振附近。过渡模式,即过渡阈值与外力振幅和频率的关系,在非常不同的物理环境下表现出显著的质的相似性。我们将自己在相对较软的圆柱形壳体中进行的荡流实验结果与早先在不同几何形状的刚性水箱中进行的实验结果进行比较,就能说明这一观察结果。根据上述相似性,我们可以假定这种转变可以通过具有通用一般结构的低阶现象动力学模型来描述。该模型的参数应取决于荡流系统的具体物理环境。建议的模型包括一个具有单向强迫的二维阻尼非线性振荡器。原始荡流系统向漩涡的过渡与简化模型中一维响应失去稳定性有关。通过多尺度扩展分析,可以在给定初始条件下将过渡阈值映射到参数平面上。结果表明,为了与现有的数值和实验结果相匹配,需要一个软化和硬化相结合的多项式模型。通过对完整的降阶模型进行直接数值模拟,结果得到了验证;并揭示了更多的响应模式。
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International Journal of Non-Linear Mechanics
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