非线性非自治系统拓扑结构分析的能量法

利用能量原理,提出一种以能量为状态参数的分析非线性非自治系统拓扑结构的定性方法。分析了能量参数确定系统状态的唯一性,揭示了能量方法的正确性和有效性以及反映系统运动状态信息的丰富性。以非自治Duffing方程为对象,采用能量状态参数,应用提出的能量方法在相空间和运动空间展开了一般的定性分析,给出了能量相图和能量时间历程、能量Poincaré截面图、能量参数分岔图,分析了其中呈现出的运动规律和捕捉到的有价值信息,并与现有的方法进行了比较。     

一种用于非线性振动系统的模态分析方法

本文提出了一种用于非线性振动系统的模态分析方法,将求解非线性系统模态的问题化为求解非线性特征值、特征向量的问题,利用模态研究系统的响应,文中分析了非线性保守系统、非线性自治系统和非线性非自治系统的线性模态,导出了三个模态包含原理。     

强非线性问题的一类能量迭代方法

基于能量原理，引进迭代及最小二乘，研究完全强非线性自治系统的周期解及其稳定性，算例表明，该法精度较高。     

热流体力学及其应用

热流体力学是一门涉及传热学、流体力学和热力学的交叉学科,并把重点放在讨论热过程对流体流动的影响。它由5部分组成:①热阻力。在某些情况下热阻力的存在对通道中的流体流量和换热系数有重大影响。借助于热阻力系数的定义和分析表达式,不仅可以预示单相通道流中的压力降,而且能用简便的方法预示气-液两相通道流中的压力降和临界热流。②热绕流。运用“虚质量源”和“热偶极子”的概念,对热绕流现象进行了分析和数值研究。它可在热除尘、粒子样品收集和热设备中流量分配等方面获得广泛的应用。③热驱动。不仅在重力场中,而且在如离心力场、表面张力场和电磁力场中也存在着热驱动流。着重讨论了流体运动的起因及其带来的后果,它包括环境污染、传热强化和同位素分离系数的提高等,④热不稳定性。重点讨论了热不稳定性的物理机理。用各种动力学方法所得到的流动不稳定性的临界准则对材料加工、热减阻、水源热污染等都是十分重要的。⑤热优化。研究了基于熵产生最小(热力学第二定律)为目标函数的流动和传热过程的优化。探讨了在一定条件下热力学第一定律效率和第二定律效率的内在联系。      

热流体力学及其应用

热流体力学是一门涉及传热学、流体力学和热力学的交叉学科,并把重点放在讨论热过程对流体流动的影响。它由5部分组成:①热阻力。在某些情况下热阻力的存在对通道中的流体流量和换热系数有重大影响。借助于热阻力系数的定义和分析表达式,不仅可以预示单相通道流中的压力降,而且能用简便的方法预示气-液两相通道流中的压力降和临界热流。②热绕流。运用“虚质量源”和“热偶极子”的概念,对热绕流现象进行了分析和数值研究。它可在热除尘、粒子样品收集和热设备中流量分配等方面获得广泛的应用。③热驱动。不仅在重力场中,而且在如离心力场、表面张力场和电磁力场中也存在着热驱动流。着重讨论了流体运动的起因及其带来的后果,它包括环境污染、传热强化和同位素分离系数的提高等,④热不稳定性。重点讨论了热不稳定性的物理机理。用各种动力学方法所得到的流动不稳定性的临界准则对材料加工、热减阻、水源热污染等都是十分重要的。⑤热优化。研究了基于熵产生最小(热力学第二定律)为目标函数的流动和传热过程的优化。探讨了在一定条件下热力学第一定律效率和第二定律效率的内在联系。     

高维含参系统的非线性振动

提出了一种适于高维一般含参系统的改进平均法，分别给出了该系统在自治及非自治情况下的非线性振动近似解的计算公式，并用该法研究了ＰＤ控制器及ＰＩＤ控制器作用下的磁力轴承转子系统的非线性振动问题．     

简谐激励下黏弹性非线性能量阱的研究

黏弹性材料作为一种良好的减振材料, 广泛应用于机械、航空和土木等领域. 本文用黏弹性Maxwell器件代替传统非线性能量阱中的阻尼元件, 提出一种新型的黏弹性非线性能量阱, 并对该模型在简谐激励下的减振性能进行分析. 首先, 根据牛顿第二定律建立系统的动力学方程, 采用谐波平衡法求解系统的幅频响应曲线, 并利用MATLAB中的Runge-Kutta数值方法验证解析解的正确性, 结果吻合良好. 然后, 分析黏弹性非线性能量阱的减振性能和参数的影响. 最后, 分析了不同质量比下非线性刚度比和阻尼比同时变化时减振效果的变化趋势, 并讨论了黏弹性非线性能量阱的最佳取值范围. 研究结果表明: 主系统的最大振幅随着非线性刚度的增加先减小后增大; 当参数选取恰当时, 黏弹性非线性能量阱比传统非线性能量阱的减振效果更优; 另外, 随着质量比的增加, 主系统最大振幅的最小值出现先减小后趋于不变的现象, 且非线性刚度比和阻尼比的最佳取值范围有所增大. 以上结论对黏弹性非线性能量阱的实际应用提供了一定的理论依据.      

岩体—界面系统剪切不稳定性分析

基于界面的刚塑性应变软化假设，分析了岩体－界面系统在端部剪力和岩体中分布剪切载荷共同作用下的变形、应力和损伤演化。利用位能原理和稳定性的能量准则，得到了岩体界面系统的不稳定性条件。分析结果表明，损伤区达到边界之前，系统可能是稳定的或者是不稳定的。依赖于分布剪切载荷和界面摩擦力的比较，若均布剪切载荷大于界面摩擦力，则系统不稳定，否则系统稳定；当损伤区达到边界之后，系统的不稳定性决定于载荷及界面材料性质，界面软化刚度系数和界面强度对于不稳定性有明显影响。     

被动隔振体非线性振动的能量迭代解法

研究了由基础振动激励、弹性材料隔离的被动隔振体的强非线性动力响应。用变形的三次多项式函数表征隔振材料的非线性刚度特性,建立了被动隔振体的非线性动力学方程,得到有阻尼受迫振动Duffing方程。将求解强非线性自治系统的能量迭代方法加以改进,推广应用到强非线性非自治系统,求出周期响应的近似解析解表达式,以及幅频关系、相频关系和隔振系数的近似表达式。算例中应用本方法与Runge-Kutta方法进行了对照,结果表明求解精度较高。本文利用计算机进行了辅助推导。     

低合金结构钢及其焊缝热影响区的韧性损伤演化行为

采用损伤力学方法研究了低合金结构钢及其焊缝热影响区近缝粗晶区的韧性损伤演化行为。从不可逆热力学出发，建立了一般韧性损伤模型。然后用一种新的交流电住损伤测量系统，测得了该钢及其模拟粗晶区的韧性损伤演化规律，得出了相应的损伤演化方程。讨论了应力三轴度对损伤演化和破坏的影响。结果表明，粗晶区及其母材的损伤分别遵循非线性和线性规律；前者的损伤生长速度远高于后者，但其临界损伤值和断裂应变远低于后者。     

Nonlinear evolution analysis of T-S disturbance wave at finite amplitude in nonparallel boundary layers

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Relaxation-Induced Suppression of Vortex Disturbances in a Molecular Gas

The influence of thermal excitation on a finite-amplitude vortex disturbance in a shear flow of a molecular gas is studied in a model problem. The evolution of such vortex structures is typical of both the nonlinear stage of the laminar–turbulent transition and for developed turbulence. Since the excitation level was assumed to be comparatively low, full Navier–Stokes equations for a compressible heat-conducting gas were used in calculations; nonequilibrium was taken into account by the coefficient of bulk viscosity. As the bulk viscosity increases in the range of realistic values, the disturbance-energy damping rate in a weakly compressible flow increases approximately by 10%. The increase in the Mach number enhances the effect of disturbance suppression.     

Linear and nonlinear approaches and digital signal processing in aeroacoustics

The linear and nonlinear approaches to the calculation of small acoustic disturbance propagation and evolution in nonuniform flows are compared. In the conventional linear approach it is the linearized equations of time-dependent, ideal (inviscid and non-heat-conducting) or viscous gas flow that are integrated. In the nonlinear approach the original nonlinear equations governing the same time-dependent flow (Euler equations for an ideal gas) are integrated; these are the same equations that, together with time relaxation procedure, are used in the linear approach for calculating the stationary background. It is shown that the application of digital signal processing, widely used in acoustic experiments, makes it possible to isolate the harmonic acoustic waves from the results of integration of the nonlinear equations, though their intensity is smaller than that of the noise due to computational errors, including inadequate attainment of the stationary background.     

刚柔耦合约束多体系统的动力分析

本文提出了描述多体系统的牵连坐标轴系统。该坐标轴系统由惯性参考系、牵连坐标系、物体坐标系及单元坐标系组成，从而实现了对刚体平动、刚体转动及弹性运动的分解，较好地消除了由于刚体大角度转动而产生的刚弹耦合非线性特性，以有限元方法为基础，应用拉格朗日方程建立了在该坐标系下的刚弹耦合约束多体系统的动力方程。该方程具有形式简洁、易于推导和编程等优点，本文并对方程的数值解法进行了研究，提出求解的广义坐标分块法，最后给出了一个典型多体系统的数值算例。     

The evolution of free-disturbances in a two-dimensional nonlinear critical layer

This paper investigates the evolution of (relatively) long Rayleigh waves on an inflectional two-dimensional boundary layer such as may occur when a flow encounters a small surface mounted obstacle. Under the assumption that the flow remains essentially two-dimensional a coupled set of evolution equations are derived that describe the nonlinear growth of an essentially arbitrary (2D) disturbance to the base flow. Numerical solutions are presented for a representative initial condition.     

Nonlinear Disturbances and Weak Discontinuities in a Supersonic Boundary Layer

The processes of wave disturbance propagation in a supersonic boundary layer with self-induced pressure [1–4] are analyzed. The application of a new mathematical apparatus, namely, the theory of characteristics for systems of differential equations with operator coefficients [5–8], makes it possible to obtain generalized characteristics of the discrete and continuous spectra of the governing system of equations. It is shown that the discontinuities in the derivatives of the solution of the boundary layer equations are concentrated on the generalized characteristics. It is established that in the process of flow evolution the amplitude of the weak discontinuity in the derivatives may increase without bound, which indicates the possibility of breaking of nonlinear waves traveling in the boundary layer.     

Uniaxial wave propagation in a nonlinear thermoviscoelastic medium with temperature dependent properties

The problem of finite wave propagation in a nonlinearly thermoviscoelastic thin rod whose viscoelastic properties are temperature dependent is considered. The rod is subjected to mechanical or thermal time-dependent loading. The coupled equations of motion and heat conduction are based on a constitutive theory of nonisothermal nonlinear viscoelasticity which is described by single-integral terms only. This theory is reformulated here for the uniaxial motion of a compressible rubbery material. The solution of the field equations is obtained by a numerical procedure which is developed for the present case and is able to handle successfully shock waves whenever they built up in the nonlinear material.     

具有精确色散性的非线性波浪数学模型

以完全非线性的自由表面边界条件为基础,以波面升高\eta和自由表面速度势\phi _\eta为待求变量,建立了新的波浪方程．方程在色散性上是完全精确的,非线性近似至三阶．与缓坡方程相比较,两者都具有精确的色散性,但该方程属于非线性模型,可模拟波浪的非线性效应,且适用于不规则波．方程的特点是属于微分-积分方程,对如何处理方程中积分项进行了讨论,并数值模拟了不同周期的线性波和二阶Stokes波,也模拟了波群的非线性演化,以对模型进行验证．      

Geometric nonlinear formulation for thermal-rigid-flexible coupling system

This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal efect. Diferent from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly,based on nonlinear strain–displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach,and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.     

Studies on nonlinear stability of three-dimensional H-type disturbance

The three-dimensional H-type nonlinear evolution process for the problem of boundary layer stability is studied by using a newly developed method called parabolic stability equations (PSE). The key initial conditions for sub-harmonic disturbances are obtained by means of the secondaryinstability theory. The initial solutions of two-dimensional harmonic waves are expressed in Landau expansions. The numerical techniques developed in this paper, including the higher order spectrum method and the more effective algebraic mapping for dealing with the problem of an infinite region, increase the numerical accuracy and the rate of convergence greatly. With the predictor-corrector approach in the marching procedure, the normalization, which is very important for PSE method, is satisfied and the stability of the numerical calculation can be assured. The effects of different pressure gradients, including the favorable and adverse pressure gradients of the basic flow, on the “H-type“ evolution are studied in detail. The results of the three-dimensional nonlinear “H-type“ evolution are given accurately and show good agreement with the data of the experiment and the results of the DNS from the curves of the amplitude variation, disturbance velocity profile and the evolution of velocity.