近空间高超声速飞行器气动特性研究的若干关键问题

在30～70 km空域机动飞行的高超声速飞行器的优点是可以耦合利用所处空域的空气产生的升力和高速飞行的离心力进行远距离机动滑翔飞行,具有重要的实用价值.尽管过去数十年在高超声速流动研究方面取得显著进展,但在设计研究近空间远程滑翔的高超声速飞行器方面仍然存在许多挑战,特别是对特定飞行条件下的流动机理了解不清楚.本文介绍了作者研究团队在开展近空间高超声速飞行器有关的关键气动问题方面的研究进展,主要包括:建立了近空间高超声速飞行的流动模型,发展了系统的相关计算空气动力学方法,针对高空高速飞行条件下稀薄气体效应和真实气体效应的耦合作用影响研究了合适的滑移边界条件,考虑了不同组分存在条件下的温度、速度和压力的滑移效应影响;提出了飞行器气动外形的动态优化方法,获得了可工程实用化的高升阻比飞行器气动外形;建立了高速飞行器动稳定性理论,在实现高超声速飞行器动态稳定飞行方面取得重大进展;最后讨论了高超声速飞行器设计中进一步需要关注的若干关键技术和科学问题、可能解决的途径及其所涉及的学科发展方向.     

近空间高超声速飞行器气动特性研究的若干关键问题

在30$\sim$70km空域机动飞行的高超声速飞行器的优点是可以耦合利用所处空域的空气产生的升力和高速飞行的离心力进行远距离机动滑翔飞行,具有重要的实用价值.尽管过去数十年在高超声速流动研究方面取得显著进展,但在设计研究近空间远程滑翔的高超声速飞行器方面仍然存在许多挑战,特别是对特定飞行条件下的流动机理了解不清楚.本文介绍了作者研究团队在开展近空间高超声速飞行器有关的关键气动问题方面的研究进展,主要包括:建立了近空间高超声速飞行的流动模型,发展了系统的相关计算空气动力学方法,针对高空高速飞行条件下稀薄气体效应和真实气体效应的耦合作用影响研究了合适的滑移边界条件,考虑了不同组分存在条件下的温度、速度和压力的滑移效应影响;提出了飞行器气动外形的动态优化方法,获得了可工程实用化的高升阻比飞行器气动外形;建立了高速飞行器动稳定性理论,在实现高超声速飞行器动态稳定飞行方面取得重大进展;最后讨论了高超声速飞行器设计中进一步需要关注的若干关键技术和科学问题、可能解决的途径及其所涉及的学科发展方向.      

基于动压约束的高超声速飞行器机动突防制导策略

针对高超声速飞行器临近空间机动突防问题,提出一种基于最低动压约束的高超声速飞行器临近空间大空域机动策略。对基于模型预测静态规划(MPSP)制导方法进行改进,末端时刻输出量考虑末端时刻时间偏差影响,性能指标函数考虑控制量输入约束影响,推导得到带多个航路点约束的扩展MPSP制导方法。根据战场态势对航路点处的动压进行约束,调节飞行轨迹的形状,实现临近空间大空域机动突防。通过仿真对所提出的制导方法有效性进行了验证,结果表明该制导方法能够很好地满足航路点处约束条件,各航路点处动压偏差在1.0 N/m~2范围内,航迹倾角偏差在0.1°范围内,高度偏差在1.0 m范围内,实现了高超声速飞行器临近空间自主机动突防。     

具有迟滞非线性的高超声速机翼颤振分析

本文采用两自由度的二元机翼模型,研究高超声速机翼由于气动弹性引起的机翼颤振问题.考虑了由于机翼连接部位的松弛和摩擦引起的机翼迟滞非线性特性的影响,采用三阶活塞理论给出高超声速机翼的非线性气动力和气动力矩.通过数值模拟,获得系统的时域响应曲线和Poincare图,分析发现,随着系统参数的变化,二元机翼会出现极限环、分岔等复杂的动力学行为,并发现迟滞非线性参数对系统极限环幅值、分岔和混沌特性有较大影响.     

高焓湍流边界层壁面摩阻产生机制分析

高超飞行器在中低空以极高马赫数飞行时,飞行器表面会遇到湍流与高温非平衡效应耦合作用的新问题.这种高焓湍流边界层壁面摩阻产生机制是新型高超声速飞行器所关注的基础科学问题,厘清此产生机制可以为减阻方法的设计提供指导,具有重要的工程实用价值.本文选取高超声速飞行时楔形体头部斜激波后的高焓流动状态,开展了考虑高温非平衡效应的湍...     

基于CFD的方形截面导弹纵向虚拟飞行模拟

通过将飞行力学模型及操纵控制舵面的控制律同流体力学方程耦合求解, 能够完成基于CFD方法的虚拟飞行模拟. 通过这种方法实现了方形截面导弹的纵向虚拟飞行模拟. 着重介绍了将飞行力学方程及舵偏控制律耦合到CFD解算器中的方法, 以及用于复杂外形的需要随飞行器及舵偏一起运动的多块结构网格更新方法,研究成果未来可用于非线性条件下飞行器稳定性及控制律的检验. 完成了方形截面导弹纵向虚拟飞行模拟,包括纵向俯仰自由度的迎角保持机动和通过舵面的偏转控制飞行器迎角按照预定的变化量减小; 通过两种典型机动动作的模拟,证明发展的耦合计算方法以及所采用的配平算法可以成功地应用于虚拟飞行模拟中.      

高超声速飞行器助推段弹道快速计算方法

为提高机动发射高超声速飞行器助推段弹道计算速度和精度,提出一种联合BP神经网络和Levenberg-Marquardt(L-M)算法实现弹道精确快速计算的方法。首先综合考虑各项约束条件设计了助推段飞行程序和弹道优化模型;其次采用BP神经网络方法推导了发射点及终端入轨点状态量与弹道参数的映射关系;最后建立了基于BP神经网络和L-M算法的联合数值寻优计算模型,并采用联合算法对高超声速飞行器助推段弹道进行优化计算。仿真结果表明,基于BP神经网络和L-M方法的联合算法能够快速和高精度地完成机动条件下的高超声速飞行器助推段弹道计算,其终端高度、速度和弹道倾角的入轨精度可分别达到2 m、0.1 m/s、0.01°,并且弹道计算耗时在3 s以内。     

轴对称转动粘弹性简支梁的稳定性分析

建立了轴对称转动粘弹性不可移简支梁的几何非线性动力学模型.应用Laplace变换和摄动法分析了超静定粘弹性杆的平衡解,得到了转动粘弹性梁的预应力平凡平衡态.应用Galerkin和摄动法得到了粘弹性梁平凡解的失稳临界值,分析了梁轴向伸长对失稳临界值的影响;通过极限分析获得了系统的后屈曲稳态近似解,讨论了平凡解二次分岔后的近似稳定吸引域,并数值仿真了系统平凡解失稳后初始挠动向稳态解的演变.本文的大范围稳定性分析发现了粘弹性系统叉式分岔失稳后的平凡态又经二次鞍结点分岔而稳定以及单向跳跃(突变)等不同于弹性系统的现象.     

高超声速湍流边界层研究现状

一、高超声速湍流边界层研究的重要性随着再入导弹武器从惯性弹道导弹发展到可作机动飞行的多弹头分导弹道导弹,以及航天飞机的出现,高超声速再入飞行器的气动外形变得更复杂了。由于出现了多个激波的相互干扰,激波与边界层的相互影响,以及边界层的分离(入射激波和后台阶产生      

双频激励下Filippov系统的非光滑簇发振荡机理

旨在揭示含双频周期激励的不同尺度Filippov系统的非光滑簇发振荡模式及分岔机制. 以Duffing和Van der Pol耦合振子作为动力系统模型,引入周期变化的双频激励项,当两激励频率与固有频率存在量级差时,将两周期激励项表示为可以作为一慢变参数的单一周期激励项的代数表达式,给出了当保持外部激励频率不变,改变参数激励频率的情况下,快子系统随慢变参数变化的平衡曲线及因系统出现的fold分岔或Hopf分岔导致的系统分岔行为的演化机制.结合转换相图和由Hopf分岔产生稳定极限环的演化过程,得到了由慢变参数确定的同宿分岔、多滑分岔的临界情形及因慢变参数改变而出现的混合振荡模式,并详细阐述了系统的簇发振荡机制和非光滑动力学行为特性.通过对比两种不同情形下的平衡曲线及分岔图,指出虽然系统有相似的平衡曲线结构, 却因参数激励频率取值的不同,致使平衡曲线发生了更多的曲折,对应的极值点的个数也有所改变,并通过数值模拟, 对结果进行了验证.      

Designing Hopf limit circle to dynamical systems via modified projective synchronization

In order to affirmatively utilize the characteristics of Hopf limit circle, a control method to design Hopf circle with proper characteristics into dynamical system is established based on the modified projective synchronization (MPS). The proposed method may serve as a complete solution to design a stable Hopf limit circle, which can simultaneously achieve the following three properties: with the desired amplitudes and shape changes, with the pre-specified location center, and at a pre-specified system parameter location. In contrast to the methods based on Hopf bifurcation theory, the new method is independent of the verbose procedures for the bifurcation critical conditions and the stability analysis. Numerical examples demonstrate the effectiveness of the proposed method.     

Bifurcations and chaotic dynamics in suspended cables under simultaneous parametric and external excitations

The bifurcations and chaotic dynamics of parametrically and externally excited suspended cables are investigated in this paper. The equations of motion governing such systems contain quadratic and cubic nonlinearities, which may result in two-to-one and one-to-one internal resonances. The Galerkin procedure is introduced to simplify the governing equations of motion to ordinary differential equations with two-degree-of-freedom. The case of one-to-one internal resonance between the modes of suspended cables, primary resonant excitation, and principal parametric excitation of suspended cables is considered. Using the method of multiple scales, a parametrically and externally excited system is transformed to the averaged equations. A pseudo arclength scheme is used to trace the branches of the equilibrium solutions and an investigation of the eigenvalues of the Jacobian matrix is used to assess their stability. The equilibrium solutions experience pitchfork, saddle-node, and Hopf bifurcations. A detailed bifurcation analysis of the dynamic (periodic and chaotic) solutions of the averaged equations is presented. Five branches of dynamic solutions are found. Three of these branches that emerge from two Hopf bifurcations and the other two are isolated. The two Hopf bifurcation points, one is supercritical Hopf bifurcation point and another is primary Hopf bifurcation point. The limit cycles undergo symmetry-breaking, cyclic-fold, and period-doubling bifurcations, whereas the chaotic attractors undergo attractor-merging, boundary crises. Simultaneous occurrence of the limit cycle and chaotic attractors, homoclinic orbits, homoclinic explosions and hyperchaos are also observed.     

BIFURCATIONS OF AIRFOIL IN INCOMPRESSIBLE FLOW

Bifurcations of an airfoil with nonlinear pitching stiffness in incompressible flow are investigated. The pitching spring is regarded as a spring with cubic stiffness. The motion equations of the airfoil are written as the four dimensional one order differential equations. Taking air speed and the linear part of pitching stiffness as the parameters, the analytic solutions of the critical boundaries of pitchfork bifurcations and Hopf bifurcations are obtained in 2 dimensional parameter plane. The stabilities of the equilibrium points and the limit cycles in different regions of 2 dimensional parameter plane are analyzed. By means of harmonic balance method, the approximate critical boundaries of 2-multiple semi-stable limit cycle bifurcations are obtained, and the bifurcation points of supercritical or subcritical Hopf bifurcation are found. Some numerical simulation results are given.     

Local stability and Hopf bifurcations analysis of the Muthuswamy-Chua-Ginoux system

The three-dimensional Muthuswamy–Chua–Ginoux (MCG, for short) circuit system based on a thermistor is a generalization of the classical Muthuswamy–Chua circuit differential system. At present, there are only partial numerical simulations for the qualitative analysis of the MCG circuit system. In this work, we study local stability and Hopf bifurcations of the MCG circuit system depending on 8 parameters. The emerging of limit cycles under zero-Hopf bifurcation and Hopf bifurcation is investigated in detail by using the averaging method and the center manifolds theory, respectively. We provide sufficient conditions for a class of the circuit systems to have a prescribed number of limit cycles bifurcating from the zero-Hopf equilibria by making use of the third-order averaging method, as well as the methods of Gröbner basis and real solution classification from symbolic computation. Such algebraic analysis allows one to study the zero-Hopf bifurcation for any other differential system in dimension 3 or higher. After, the classical Hopf bifurcation of the circuit system is analyzed by computing the first three focus quantities near the Hopf equilibria. Some examples and numerical simulations are presented to verify the established theoretical results.

     

Hopf分岔的代数判据及其在车辆动力学中的应用

利用Hurwitz行列式,给出平衡点失稳而发生Hopf分岔的代数判定准则和计算方法,这一方法将Hopf分岔点的求解转化为一个非线性方程的求解问题,从而克服了以前方法在计算Hopf分岔点时,对于参数的每一次变化通过求特征根并判定特征根的实部是否为零的庞大工作量。应用这一方法,我们进行了非线性车辆系统蛇行运动稳定性的研究,得到了轮对系统发生蛇行运动的临界速度的解析表达式。     

Two-parameter bifurcation analysis of limit cycles of a simplified railway wheelset model

The effect of the nonlinear terms on bifurcation behaviors of limit cycles of a simplified railway wheelset model is investigated. At first, the stable equilibrium state loses its stability via a Hopf bifurcation. The bifurcation curve is divided into a supercritical branch and a subcritical one by a generalized Hopf point, which plays a key role in determining the occurrence of flange contact and derailment of high-speed railway vehicles, and the occurrence of this critical situation is an important decision-making criteria for design parameters. Secondly, bifurcations of limit cycles are discussed by comparing the bifurcation behavior of cycles for two different nonlinear parameters. Unlike local Hopf bifurcation analysis based on a single bifurcation parameter in most papers, global bifurcation analysis of limit cycles based on two bifurcation parameters is investigated, simultaneously. It is shown that changing nonlinear parameter terms can affect bifurcation types of cycles and division of parameter domains. In particular, near the branch points of cycles, two symmetrical limit cycles are created by a pitchfork bifurcation and then two symmetrical cycles both undergo a period-doubling bifurcation to form two stable period-two cycles. Around the resonant points, period orbits can make several turns, whose number of turns corresponds to the ratio of resonance. Thirdly, near the Neimark–Sacker bifurcation of cycles, a stable torus is created by a supercritical Neimark–Sacker bifurcation, which shows that the orbit of the model exhibits modulated oscillations with two frequencies near the limit cycle. These results demonstrate that nonlinear parameter terms can produce very complex global bifurcation phenomena and make obvious effects on possible hunting motions even though a simple railway wheelset model is concerned.

     

轮对非线性动力学模型稳定性和分岔特性研究

为了探究轮对系统的横向失稳问题,考虑了陀螺效应和一系悬挂阻尼的影响作用,建立非线性轮轨接触关系的轮对动力学模型,研究轮对系统的蛇行稳定性、Hopf分岔特性及迁移转化机理.通过稳定性判据获得了轮对系统失稳临界速度.采用中心流形定理和规范型方法对轮对动力学模型进行化简,得到与轮对系统分岔特性相同的一维复变量方程,理论推导求得轮对系统的第一Lyapunov系数的表达式,根据其符号即可判断轮对系统的Hopf分岔类型.讨论了不同参数对轮对系统Hopf分岔临界速度的影响,探究了轮对系统的超临界、亚临界Hopf分岔域在二维参数空间的分布规律.利用数值模拟得到轮对系统的3种典型Hopf分岔图,验证了轮对系统超临界、亚临界Hopf分岔域分布规律的正确性.结果表明,轮对系统的临界速度随着等效锥度的增大而减小,随着一系悬挂的纵向刚度和纵向阻尼的增大而增大,随着纵向蠕滑系数的增大呈先增大后减小.系统参数变化会引起轮对系统Hopf分岔类型发生改变,即亚临界与超临界Hopf分岔相互迁移转化.轮对系统Hopf分岔域在二维参数空间的分布规律对于轮对系统参数匹配和优化设计具有一定的指导意义.     

Double Hopf Bifurcation Analysis Using Frequency Domain Methods

The dynamic behavior close to a non-resonant double Hopf bifurcation is analyzed via a frequency-domain technique. Approximate expressions of the periodic solutions are computed using the higher order harmonic balance method while their accuracy and stability have been evaluated through the calculation of the multipliers of the monodromy matrix. Furthermore, the detection of secondary Hopf or torus bifurcations (Neimark–Sacker bifurcation for maps) close to the analyzed singularity has been obtained for a coupled electrical oscillatory circuit. Then, quasi-periodic solutions are likely to exist in certain regions of the parameter space. Extending this analysis to the unfolding of the 1:1 resonant double Hopf bifurcation, cyclic fold and torus bifurcations have also been detected in a controlled oscillatory coupled electrical circuit. The comparison of the results obtained with the suggested technique, and with continuation software packages, has been included.     

Hopf Bifurcation in a Diffusive Logistic Equation with Mixed Delayed and Instantaneous Density Dependence

A diffusive logistic equation with mixed delayed and instantaneous density dependence and Dirichlet boundary condition is considered. The stability of the unique positive steady state solution and the occurrence of Hopf bifurcation from this positive steady state solution are obtained by a detailed analysis of the characteristic equation. The direction of the Hopf bifurcation and the stability of the bifurcating periodic orbits are derived by the center manifold theory and normal form method. In particular, the global continuation of the Hopf bifurcation branches are investigated with a careful estimate of the bounds and periods of the periodic orbits, and the existence of multiple periodic orbits are shown.