Limit cycle oscillation suppression of 2-DOF airfoil using nonlinear energy sink

This paper presents a novel mechanical attachment, i.e., nonlinear energy sink （NES）, for suppressing the limit cycle oscillation （LCO） of an airfoil. The dynamic responses of a two-degree-of-freedom （2-DOF） airfoil coupled with an NES are studied with the harmonic balance method. Different structure parameters of the NES, i.e., mass ratio between the NES and airfoil, NES offset, NES damping, and nonlinear stiffness in the NES, are chosen for studying the effect of the LCO suppression on an aeroelastic system with a supercritical Hopf bifurcation or subcritical Hopf bifurcation, respectively. The results show that the structural parameters of the NES have different influence on the supercritical Hopf bifurcation system and the subcritical Hopf bifurcation system.

Vortex-Induced Vibration of a Tension Leg Platform Tendon:Multi-Mode Limit Cycle Oscillations

This paper studies the application of mathematical models to analyze the vortex-induced vibrations of the tendons of a given TLP along the Indian coastline, by using an analytical approach, using MATLAB. The tendon is subjected to a steady current load, which causes vortex-shedding downstream, leading to cross-flow vibrations. The magnitude of the excitation(lift and drag coefficients) depends on the vortex-shedding frequency. The resulting vibration is studied for possible resonant behavior. The excitation force is quantified empirically, the added mass by potential flow hydrodynamics, and the vibration by normal mode summation method. Non-linear viscous damping of the water is considered. The non-linear oscillations are studied by the phase-plane method, investigating the limit-cycle oscillations. The stable/unstable regions of the dynamic behavior are demarcated. The modal contribution to the total deflection is studied to establish the possibility of resonance of one of the wet modes with the vortex-shedding frequency.

Analysis of limit cycle oscillations of a typical airfoil section with freeplay

A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the non- linearity of the airfoil section＇s freeplay. There are two crit- ical speeds in the system, i.e., a lower critical speed, above which the system might generate limit cycle oscillation, and an upper critical one, above which the system will flutter. Then a Poincar6 map is constructed for the limit cycle os- cillations by using piecewise-linear solutions with and with- out contact in the system. Through analysis of the Poincar6 map, a series of equations which can determine the frequen- cies of period-1 limit cycle oscillations at any flight veloc- ity are derived. Finally, these analytic results are compared to the results of numerical simulations, and a good agree- ment is found. The effects of freeplay value and contact stiffness ratio on the limit cycle oscillation are also analyzed through numerical simulations of the original system. More- over, there exist multi-periods limit cycle oscillations and even complicated ＂chaotic＂ oscillations may occur, which are usually found in smooth nonlinear dynamic systems.

Reversed rotation of limit cycle oscillation and dynamics of low-intermediate-high confinement transition

The dynamics of the confinement transition from L mode to H mode（LH） is investigated in detail theoretically via the extended three-wave coupling model describing the interaction of turbulence and zonal flow（ZF） for the first time.Thereinto, turbulence is divided into a positive-frequency（PF） wave and a negative-frequency（NF） one, and the gradient of pressure is added as the auxiliary energy for the system. The LH confinement transition is observed for a sufficiently high input energy. Moreover, it is found that the rotation direction of the limit cycle oscillation（LCO） of PF wave and pressure gradient is reversed during the transition. The mechanism is illustrated by exploring the wave phases. The results presented here provide a new insight into the analysis of the LH transition, which is helpful for the experiments on the fusion devices.

NONLINEAR ANALYSIS OF EQUATORIAL EASTERN PACIFIC AIR-SEA COUPLING OSCILLATION AND A LIMIT-CYCLE THEORY FOR ENSO CYCLE

The troposphere and ocean mixed layer were considered as two components of a dynamic system operated by solar radiation as the constant source of energy, where upon an air-sea coupling self-exited coupling oscillation model was based with the aid of a locally averaged thermodynamic climate model, resulting mathematically in a closed self-governed dynamic system, a so-called El Nino-Southern Oscillation(ENSO) system. With the limit cycle solution of the system. It is shown that the essential physics of the coupled system can be described by the ENSO system. Compared with the observations, the theoretical limit cycle orbit matches the observed phase loop qualitatively. The ENSO system provides a useful theoretical framework for study of interannual variation of the tropical climate system.

Non-linear 2-DOF model and centre manifold theory to study limit cycle oscillations caused by drum-brake judder

This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to describe the low-frequency vibration of the drum brake, applied the centre manifold theory to simplify the system, and obtained the LCO amplitude by calculating the normal form of the simplified system at the Hopf bifurcation point. It is indicated that when the friction coefficient is smaller than the friction coefficient at the bifurcation point, the amplitude decreases; whereas with a friction coefficient larger than the friction coefficient of bifurcation point, LCO occurs. The results suggest that it is applicable to suppress the LCO amplitude by changing systematic parameters, and thus improve the safety and ride comfort when applying brake. These findings can be applied to guiding the design of drum brakes.

Generation of Optimal Voltage Reference for Limit Cycle Oscillation in Digital Control-Based Switching Power Supply

Digital control of a general-purpose switching power supply is one of the key technologies to perform the high reliability and the intelligent function demanded for the next generation. The contribution of this paper is the development of a digital control-based switching power supply. In the developed system, the generation method of the optimal voltage reference to eliminate the limit cycle oscillation of output voltage due to the AD/DA resolution is proposed. In the proposed method, the variation of the input power source voltage can be also compensated. The effectiveness of the proposed optimal reference generation method is experimentally verified.

Nonlinearity and periodic solution of a standard-beam balance oscillation system

We present the motion equation of the standard-beam balance oscillation system, whose beam and suspensions, compared with the compound pendulum, are connected flexibly and vertically. The nonlinearity and the periodic solution of the equation are discussed by the phase-plane analysis. We find that this kind of oscillation can be equivalent to a standard-beam compound pendulum without suspensions; however, the equivalent mass centre of the standard beam is extended. The derived periodic solution shows that the oscillation period is tightly related to the initial pivot energy and several systemic parameters： beam length, masses of the beam, and suspensions, and the beam mass centre. A numerical example is calculated.

A nonlinear POD reduced order model for limit cycle oscillation prediction

As the amplitude of the unsteady flow oscillation is large or large changes occur in the mean background flow such as limit cycle oscillation,the traditional proper orthogonal decomposition reduced order model based on linearized time or frequency domain small disturbance solvers can not capture the main nonlinear features.A new nonlinear reduced order model based on the dynamically nonlinear flow equation was investigated.The nonlinear second order snapshot equation in the time domain for proper orthogonal decomposition basis construction was obtained from the Taylor series expansion of the flow solver.The NLR 7301 airfoil configuration and Goland+ wing/store aeroelastic model were used to validate the capability and efficiency of the new nonlinear reduced order model.The simulation results indicate that the proposed new reduced order model can capture the limit cycle oscillation of aeroelastic system very well,while the traditional proper orthogonal decomposition reduced order model will lose effectiveness.

Calculations of the bounds on limit cycle oscillations in nonlinear aeroelastic systems based on equivalent linearization

The nonlinear aeroelastic system of an airfoil with an external store was investigated,with emphasis on the bounds of limit cycle oscillations(LCOs).Based on the equivalent linearization,an approach was proposed to calculate the bounds on LCOs over the full flight envelope.The bounds are determined directly without solving LCOs one by one as the flow speed varies.The presented approach can provide us with the maximal LCO amplitudes and the lower threshold for flow speed beyond which LCOs may arise.Numerical examples show that the obtained bounds are in nice agreement with numerical simulation results.The speed threshold can be predicted to a relative error less than 0.1%,and the maximal LCO amplitude to about 3%.The influences of the system parameters on the speed threshold for speed were investigated efficiently by the proposed approach.

LCO—颤振试飞中一种典型非线性气弹现象探究

首先对非线性气动弹性分类和极限环振荡(LCO)的发生机理进行了简要介绍,进而对某型飞机颤振飞行试验中遇到的极限环振荡现象进行了详细分析,最后对在颤振试飞中遇到极限环振荡现象时的处置措施和相应颤振飞行试验的工作方法给出一些建议。

LCO flutter of cantilevered woven glass/epoxy laminate in subsonic flow

The paper presents a cantilevered composite wing, aeroelastic characteristics of idealized as a composite flat plate laminate. The composite laminate was made from woven glass fibers with epoxy matrix. The elastic and dynamic properties of the laminate were determined experimentally for aeroelastic calculations. Aeroelastic wind tunnel testing of the laminate was performed and the result showed that flutter, a dynamic instability occurred. The cantilevered laminate also displayed limit cycle amplitude, post-flutter oscillation. The experimental flutter velocity and frequency were verified by our computational analysis.

基于流固耦合的压气机转子叶片非同步振动分析

压气机转子叶片非同步振动是近年来发现的一类新气动弹性问题,表现为叶片振动频率与转频不同步且具有锁频现象,严重影响航空发动机的可靠性和运行安全,目前对其产生机理并不完全清楚.为了深入研究压气机内不稳定流动与叶片非同步振动之间的耦合机制,基于时间推进的方法建立了多级压气机转子叶片全环的双向流固耦合模型,数值研究了刚性叶片与非同步振动柔性叶片的非定常流场、气流激励频率和结构响应特征,揭示了压气机转子叶片非同步振动的流固耦合机制.结果表明:近失速工况下,转子叶尖吸力面径向分离涡的周期性脱落及再附过程是导致叶尖压力剧烈波动的主要原因,其3倍谐波激励频率与转子一阶弯曲固有频率接近,提供了叶片非同步振动的初始气流激励源.叶片非同步振动发生时,位移响应表现为等幅值的极限环特征,振动以一阶弯曲模态主导,径向分离涡产生的非整数倍气流激励频率及其谐波频率最终锁定为叶片一阶弯曲固有频率,非同步振动的运动胁迫使得相邻通道叶尖流场周向趋于一致.研究成果及对叶片非同步振动流固耦合机制的认识可为压气机内部不稳定流动诱发的叶片振动失效分析提供有益参考.

高速飞行器间隙非线性机翼颤振的非线性能量阱抑制

针对间隙非线性机翼颤振系统的亚临界问题,引入了非线性能量阱(nonlinear energy sink,NES)技术来提高系统发生极限环振荡的临界速度。建立了具有NES控制的间隙非线性机翼颤振系统动力学模型,并分析了质量比、频率比、阻尼比、相对位置等NES参数对颤振系统极限环振荡的抑制效果,以及NES参数对颤振系统极限环振荡临界速度的影响规律。结果表明,阻尼比越大,可以在越小的自振频率比情况下使系统进入稳定区,但需要更苛刻的NES位置要求,即越靠近机翼前缘;而阻尼比越小,则使颤振系统极限环振荡响应进入稳定区所需的NES质量越小。在NES位置靠近机翼前缘时,增大自振频率比会使极限环振荡抑制效果有明显的提升,而增大质量比可以显著提高极限环振荡的抑制效果和临界速度。此外,NES的阻尼比越小,其颤振系统的极限环振荡抑制效果越好。

不同折叠角下含间隙折叠机翼极限环振荡分析

折叠机翼作为变体飞行器的重要变体机构之一,其气动弹性响应规律研究为变体飞行器稳定性及操纵性的提升奠定基础。本文提出基于干风洞的含间隙折叠机翼地面颤振虚拟试验模型建模方法,其中折叠机翼翼面子结构采用Craig-Bampton方法建立其刚柔耦合降阶模型,子结构连接采用线性/非线性弹簧连接,气动力采用偶极子格网法获得并转化为激振器集中力,由于地面颤振试验中气动力建模需基于统一的模态振型,针对含间隙折叠机翼采用虚拟质量法获得统一坐标下的虚拟模态振型。仿真结果表明,基于Craig-Bampton方法建立的线性折叠机翼地面颤振虚拟试验模型预测颤振速度与商用软件相比误差低于2%。当模型中采用非线性弹簧连接时,折叠机翼在低于和高于线性颤振速度下均会形成极限环振荡,仿真表明由于间隙非线性的影响,极限环的临界速度比线性颤振降低。研究发现折叠角0°下间隙大小对极限环幅值具有显著影响,而折叠角30°下间隙大小则对极限环幅值几乎不产生影响。

Multiple Limit Cycles in an Immune System

The nonlinear oscillatory phenomenon has been observed in the system of immune response, which corresponds to the limit cycles in the mathematical models. We prove that the system simulating an immune response studied by Huang has at least three limit cycles in the system. The conditions for the multiple limit cycles are useful in analyzing the nonlinear oscillation in immune response.

Van der Pol-Duffing系统的非共振Hopf分叉

用多尺度法求出了系统的一次近似平均方程和极坐标形成的分叉响应方程。研究了系统非共振情况下的平衡点性质和Hopf分叉 。

电液伺服系统非线性振动机理及试验研究

电液伺服系统是非线性动力学系统,在工作过程中容易出现非线性振动、噪声、冲击和爬行等异常现象,而且诱因不易确定,严重影响系统的稳定性。根据非线性动力学原理,建立电液伺服系统的非线性动力学模型。通过理论研究,探索非线性液压弹簧力和非线性摩擦力等非线性因素对系统动力学特性的影响规律。指出非线性液压弹簧力作用可以用Duffing方程描述,非线性摩擦力作用可以用Van Der Pol方程描述。用研究非线性动力学系统的有效方法:时间历程、频闪采样、功率谱等,对实测信号进行深入分析,多方位揭示电液伺服系统非线性振动的机理及诱因。结果表明,非线性液压弹簧力引起的'跳跃现象'和非线性摩擦力引起的极限环型振荡的共同作用是导致系统发生非线性振动的一个主要诱因,值得关注。

基于模态耦合的摩擦自激振荡系统稳定性研究

模态耦合是摩擦引起系统自激振荡的主要不稳定性机理之一。针对此类问题,构建了两自由度非线性质量-传动带系统。首先,通过劳斯判据分析系统的稳定性,给出了计算Hopf分岔点的数学表达式以及系统参数改变时分岔点和特征值分岔图的变化状态。其次,将扩展谐波平衡法加以利用和延伸,得到了自激振荡系统极限环幅值的解析解,进而研究了系统外界参数和结构参数变化对极限环幅值的影响。外界参数(带速和摩擦系数)变化可造成极限环幅值的规律性变化,而结构参数(阻尼比和固有频率)的改变会引起极限环幅值复杂的动力学行为。研究方法及结果可为机械系统结构设计和减振等方面提供理论分析参考。

铜电极阳极溶解过程恒电位电流振荡的动力学模型

研究了铜电极在酸性氯化钠溶液中的恒电位电流振荡行为 ,分析了电极过程中的非线性步骤及电化学耦合因素 ,提出了一个可能的电极过程动力学模型 ,并借助线性稳定性分析及分支分析得到了参数坐标空间中的动力学行为区域图 .在此基础上 ,将极化曲线视为稳定非平衡定态区态函 (电流 )与外控参数 (电位 )的关系 ,同时将恒电位电流振荡模拟为稳定极限环振荡 ,分别计算出了极化曲线与时间 -电流振荡曲线 ,其结果与实验数据相符 ,表明该类电极过程中的电化学振荡的理论研究可以纳入