考虑剪切和翘曲影响的直升机旋翼气弹稳定性分析

在中等变形梁理论的基础上,对桨叶变形体进行有限变形分析,推导出同时考虑剪切和翘曲影响的小应变、中等变形梁应变-位移关系,并构造出一个全新的21自由度梁单元,应用Hamilton原理导出桨叶运动的有限元方程。在此基础上,研究了剪切和翘曲等非经典因素对无铰旋翼桨叶的动特性和悬停时气弹稳定性的影响。数值结果表明:剪切和翘曲对旋转桨叶的固有频率,尤其是高阶频率,有一定的影响,特别是随着转速的提高这种影响会变大;同时对悬停时桨叶的气弹稳定性有相当程度的影响,尤其是在高桨距角下这种影响是不能忽略的。     

多点敷设支撑层的粘弹性约束阻尼梁振动分析

针对夹层约束阻尼梁结构的减振特性进行深入研究,在其基础上扩展多处敷设增设支撑层的约束阻尼,建立了多点铺设增设支撑层约束阻尼梁的振动特性模型,利用粘弹性材料的Maxwell模型、假设模态法、有限元理论和力学原理,结合功能特性方程和Lagrange方程,导出了增设支撑层约束阻尼梁的振动位移响应方程.通过对敷设双支撑约束阻尼简支梁在支撑层厚度变化的参数研究,可以看到增设适当厚度的支撑层能够达到更好的减振效果.     

Large Amplitude Flexural Vibration of the Orthotropic Composite Plate Embedded with Shape Memory Alloy Fibers

研究了形状记忆合金(SMA)纤维混杂复合材料大挠度层合板的非线性自由与受迫振动特性。基于描述SMA力学行为的Brinson理论以及层合板材料性能预测的混合率,建立了SMA纤维混杂复合材料大挠度层合板的本构方程,基于对称层合各向异性弹性板的非线性理论,建立了以横向挠度和应力函数表示的板的横向振动方程和相容方程。采用Galerkin近似解法将振动方程化为时间变量的含有3次非线性项的Duffing型常微分方程,采用谐波平衡法(HBM)获得系统的固有频率方程和强迫振动稳态频率响应方程。数值计算表明,非线性板自由振动频率比与激励温度的关系具有与线性板相同的特征,马氏体相向奥氏体相转变阶段温度对板的振动频响特性曲线的影响最显著,同时也讨论了SMA纤维含量、板的纵横比以及自由振动幅值对板的非线性频率比的影响。     

具有电磁约束阻尼层梁的振动主动控制研究计算(英文)

This paper investigates vibration control of beam through electro-magnetic constrained layer damping （EMCLD） which consists of electromagnet layer, permanent magnet layer and viscoelastic damping layer. When the coil of the electromagnet is electrified with proper control strategy, the electromagnet can exert magnetic force opposite to the direction of structural deformation so that the structural vibration is attenuated. A mathematical model is developed based on the equivalent current method to calculate the electromagnetic control force produced by EMCLD. The governing equations of the system are obtained using Hamilton＇s Principle and then reduced with the assumed-mode method. A simulation on vibration control of a cantilever beam is conducted under the velocity proportional feedback to demonstrate the energy dissipation capability of EMCLD, and the beam system with the same parameter is experimented. The results of experiment and simulation are compared and the results show that the EMCLD is an effective means for suppressing modal vibration. The results also indicate that the beam system has better control performance for larger control current. The EMCLD method presented in this paper provides an applicable and efficient tool for the vibration control of structures.     

旋转Timoshenko梁的动力学分析

针对旋转Timoshenko梁结构,在梁的纵向、横向变形中均考虑横向弯曲以及轴向伸缩的耦合作用,同时在横向弯曲中考虑剪切变形的影响,在柔性梁的2个变形方向上均考虑了变形的二次耦合项,并充分考虑轴向离心力、横向惯性力的作用,利用有限元方法进行离散并利用Hamilton原理建立非线性变形模式下的一种新的Timoshenko梁动力学方程。对一平面旋转梁进行仿真计算,通过分析不同情况下的频率与端点变形位移,说明耦合作用的"软化"效果,以及轴向离心力、横向惯性力对模型的影响。     

离心压气机S1流面流场的计算

本文对计算轴流压气机 S1流面的流函数矩阵解法的计算机程序作了修改,使之能适合于计算离心压气机的 S1流面。本方法是引入人工密度,积分运动方程求速度场,而后求密度场,进行迭代求解,计算速度非常迅速。对离心压气机的几个算例表明:只要不发生明显分离,计算结果与实验值是符合的。      

Geometrically exact nonlinear analysis of pre-twisted composite rotor blades

Modeling of pre-twisted composite rotor blades is very complicated not only because of the geometric non-linearity, but also because of the cross-sectional warping and the transverse shear deformation caused by the anisotropic material properties. In this paper, the geometrically exact nonlinear modeling of a generalized Timoshenko beam with arbitrary cross-sectional shape, generally anisotropic material behavior and large deflections has been presented based on Hodges’ method. The concept of decomposition of rotation tensor was used to express the strain in the beam. The variational asymptotic method was used to determine the arbitrary warping of the beam cross section. The generalized Timoshenko strain energy was derived from the equilibrium equations and the second-order asymptotically correct strain energy. The geometrically exact nonlinear equations of motion were established by Hamilton’s principle. The established modeling was used for the static and dynamic analysis of pre-twisted composite rotor blades, and the analytical results were validated based on experimental data. The influences of the transverse shear deformation on the pre-twisted composite rotor blade were investigated. The results indicate that the influences of the transverse shear deformation on the static deformation and the natural frequencies of the pre-twisted composite rotor blade are related to the length to chord ratio of the blade.     

Stochastic analysis of two dimensional nonlinear panels with structural damping under random excitation

Stochastic behavior of panels in supersonic flow is investigated to assess the significance of including the damping caused by the strains resulting from axial extension of the panel. The governing equations of motion are based on the Von Karman's large deflection equation and are considered with Kelvin's model of structural damping. The panel under study is two dimensional and simply supported for which the first order piston theory is used to account for the unsteady aerodynamic loading. Transformation of the governing partial differential equation to a set of ordinary differential equations is performed through the Galerkin averaging technique. The statistical response moment equations are generated for two modes using the Fokker–Planck equation with a Gaussian closure scheme. The response moments history and their steady state values are considered. Comparison with previous studies shows that the new nonlinear damping term developed through modeling has a significant effect on the response moments. This is verified through analysis of the effects of external pressure and in-plane force spectral density, air-to-structure mass ratio and structural damping ratio on the mean square value of modal amplitudes.     

粘弹壁板颤振的非线性动力特性

研究粘弹材料壁板在超声速气流作用下颤振时的分岔及混沌等复杂动力学特性。采用von Karman大变形理论及Kelvin粘弹阻尼模型建立壁板的动力学方程,通过线性活塞理论建立气动力模型。利用迦辽金法将壁板颤振模型转化为常微分方程组,并使用Gear的BDF方法进行数值求解。通过数值模拟研究了该系统在粘弹阻尼作用下的动力学行为以及粘弹阻尼的影响。计算结果表明,粘弹壁板颤振系统表现出丰富的动力学行为,其二次分岔特性很复杂。随着粘弹性阻尼的增大,系统的稳定解区域在减小,而静态屈曲解几乎不受影响,同时发现混沌运动区域也随着粘弹阻尼的增大而减小。     

Free vibration of triply coupled centrifugally stiffened nonuniform beams,using a refined dynamic finite element method

The application of a Refined Dynamic Finite Element (RDFE) technique to triply coupled vibration of centrifugally stiffened beams is presented. The proposed method is a fusion of the “Galerkin weighted residual” formulation and the Dynamic Stiffness Matrix (DSM) method, where the basis functions of approximation space are assumed to be the closed form solutions of the differential equations governing uncoupled bending and torsional vibrations of the beam. The use of resulting dynamic trigonometric interpolation (shape) functions leads to a frequency dependent stiffness matrix, representing both mass and stiffness properties of the beam element. Assembly of the element matrices and the application of the boundary conditions then leads to a frequency dependent nonlinear eigenproblem. The Wittrick–Williams algorithm is used as a solution technique to compute the natural frequencies and modes of five illustrative example beam configurations, exhibiting doubly and triply coupled vibrations. The discussion of results is followed by some concluding remarks.     

求解平面翼型亚,跨声速绕流的一个新方法

本文提出了求解平面翼型亚、跨声速绕流的一个新方法。引入流函数和Ｖｏｎ Ｍｉｓｅｓ变换后，亚、跨声速绕机翼无旋流动的基本方程组被化为以流线纵坐标ｙ为未知量的单个二阶偏微分方程－流线控制方程。并通过变换将物理平面上的无限域变为计算平面上有限的矩形域，而后在计算平面采用有限差分线松弛迭代法求解。作为算例，计算了对称翼型ＮＡＣＡ００１２－３４和非对称翼型ＮＡＣＡ４４１２的亚、跨声速有攻角绕流，所得数值结果     

CFRP反射器型面主动控制和作动器位置优化

研究了运用压电陶瓷作动器对碳纤维增强复合材料（CFRP）格栅反射器的型面主动控制。首先，采用了一种具有独立电压自由度的梁单元，以及考虑高阶剪切变形的板单元，对主控格栅反射器进行有限元建模；运用能量变分哈密尔顿原理推导了主控格栅反射器的有限元控制方程，并给出了反射面型面残余均方根（RMS）误差最小的电压最优控制方法。然后，研究了在典型载荷下，反射面残余RMS误差最小的PZT作动器位置分布的优化配置问题；提出了一种将遗传算法和梯度投影方法相结合的改进优化方法，用来求出在限定作动器数量的条件下，作动器几何位置的优化配置，使控制后反射面的残余RMS误差最小；给出的数值算例验证了方法的正确性和有效性。最后，研制了格栅反射器型面主动控制的实验样机，针对反射器的初始制造误差进行了型面主动控制，验证了控制方法的可行性和有效性。     

特定工况下内嵌钢球欧拉梁碰撞减振性能研究

针对内嵌自主移动钢球欧拉梁碰撞系统,研究了在一复杂工况下内嵌自主移动钢球碰撞阻尼机制对梁残余衰减振动的抑制效果.采用线性弹簧-阻尼模型模拟钢球与梁之间的碰撞机制,通过分析建立了整个碰撞系统的分段线性动力学方程,并运用无量纲化、假设模态法、高阶模态截断等方法导出了系统的状态空间方程.数值计算结果充分表明在此工况下内嵌自主...     

Vibrations of an elastic guide beam with a missile moving along it

Transverse nonstationary vibrations of a guide beam having the initial flexure are considered. An absolutely rigid missile moves under the propulsive force along this guide beam on two sliding supports. The beam displacements introduced by its vibrations are presented as an expansion with respect to the given functions according to the Ritz method. The equations of nonstationary vibration of the beam with the missile moving along it are obtained in the generalized coordinates, the expansion coefficients being chosen as them. The example is presented. Also studied is the effect of different beam and missile parameters on the beam displacement and transverse and angular velocity of the missile.     

两端铰支输流管道固有频率的研究

利用复模态分析方法和Galerkin方法研究了两端铰支输流管横向振动对其固有频率的影响.通过数值方法绘出系统的前两阶固有频率随流体速度的变化情况.利用数值算例分析了复模态分析方法、二阶Galerkin截断和四阶Galerkin截断方法对固有频率的影响.     

弧齿圆锥齿轮传动的振动分析

 考虑了齿轮体在各个方向的线振动和角振动,以及齿轮辐板和输入轴、输出轴的扭转变形,以弧齿锥齿轮传动系为对象,建立了一个多刚体多自由度的振动系统模型,推导了这一系统的参数激励微分方程组。再将方程组转化为线性定常的形式,并将参数激励转化为外激励,成功地求解了弧齿锥齿轮传动系统的振动过程。     

可靠性灵敏度分析的一种新方法

基于极限状态函数矩估计的失效概率计算,提出一种新的可靠性灵敏度分析方法。推导极限状态函数的矩对基本变量分布参数的偏导数,并进而利用失效概率与极限状态方程矩的关系,推导失效概率对基本变量分布参数的偏导数,从而得到可靠性灵敏度。与改进一次二阶矩可靠性灵敏度分析方法相比,所提方法不用求极限状态方程的设计点,因而不需用到极限状态函数对基本变量的梯度函数,适用于隐式极限状态方程的可靠性灵敏度分析,算例结果也充分显示所提方法的合理性和精度。     

自由阻尼梁高频能量流响应的解析模型

针对自由阻尼梁的高频振动问题，基于波动理论提出了大阻尼复合结构的能量流解析模型。利用等效复刚度方法确定了完全自由阻尼梁结构的等效弯曲刚度和损耗因子，基于能量流分析方法构建了结构的能量密度控制方程，求解了结构的高频能量流响应。分析了弯曲波在阻尼结构耦合处的能量传递特性，构建了局部自由阻尼梁的高频能量流解析模型，预测了大阻尼耦合结构的高频振动特性。数值结果表明，提出的能量流解析解与经典的时空平均波动解一致逼近，因而能够精确地预测自由阻尼梁等大阻尼复合结构的高频能量流响应。     

N-S方程有限分析数值研究

 本文将有限分析方法用于曲线座标系上紊流N-S方程的数值计算。分别计算了单列和串列叶栅内部流场,计算中采用了k-ε紊流模型和壁面函数。计算结果与试验结果相比较,吻合程度令人满意。有限分析方法在网格单元上对N-S方程进行线化处理,以解析边界条件作为约束,得出解析解,在解析解基础上构造离散代数方程。有限分析方法的最大特点是可以适应对流速度大小和方向,自动调整格式系数,因而具有数值扩散小和稳定性高等优点。     

涡轮气热弹耦合计算模型与算例

针对涡轮气热弹多场耦合不变量方程,推导了任意曲线坐标系中的多场耦合控制方程,讨论了气热弹多场耦合的4种类型：气热、气弹、热弹和气热弹耦合,给出了相应的计算模型与耦合边界条件,建立了能够采用统一差分格式求解涡轮气热弹多场耦合的三维数值仿真平台的计算模型。并通过对一个具有解析解空心圆筒的热弹性计算和对Mark Ⅱ叶片气热耦合计算,初步验证了应用有限差分计算气热弹多场耦合计算模型的可行性。