在中面载荷作用下正交各向异性矩形板后屈曲行为分析

本文利用摄动法和广义傅氏级数法分析了在中面载荷作用下正交各向异性矩形板后屈曲行为,对几种典型的纤维增强环氧复合材料矩形板后屈曲行为给出了结果,可供工程设计应用参考。     

变厚度弹性件柔性接头的非线性分析

结合试验数据,采用Mooney-Rivlin模型模拟了柔性接头的弹性件材料;根据非线性理论,采用混合插值有限元法对某一摆角状态下的柔性接头进行了大变形非线性弹性分析,并在此基础上初步探讨了厚度不均匀弹性件对层间应力的影响。计算结果表明,弹性层减薄到一定程度时,层间剪切应力沿宽度方向分布变得均匀,应力值仍集中在2 MPa以下;层间法向应力分布变化较小,呈二次曲线分布,最大值有所降低;其中,接近后法兰的弹性件厚度不均时,对各项应力最大值影响较大。     

基于Reddy简化高阶剪切理论的复合材料对称角铺设矩形板横向弯曲一般解析解

采用复数级数法求解基于Reddy简化高阶剪切理论的复合材料对称角铺设矩形板横向弯曲问题。将待定位移函数展开为复数级数,代入该弯曲问题控制偏微分方程组,确定特征根和挠度待定常数与其他位移函数待定常数之间关系式。首次给出了该弯曲问题实数形式的一般解析解。将该一般解析解代入矩形板弯曲边界条件和角点条件,根据正弦级数的正交性建立关于挠度函数待定常数的线性代数方程组,求解此线性代数方程组可确定挠度函数待定常数。建立了该问题解析求解模式。将Reddy高阶剪切理论解析解与经典理论、一阶剪切理论解析解进行对比计算,验证了一般解析解,并给出数值算例。     

On hydromagnetic flow of an Oldroyd-B fluid near a pulsating plate

An initial value investigation is made of the motion of an incompressible, viscoelastic, conducting Oldroyd-B fluid bounded by an infinite rigid non-conducting plate. The unsteady flow is generated from rest in the fluid due to velocity tooth pulses subjected on the plate in presence of an external magnetic field. It is assumed that no external electric field is acting on the system and the magnetic Reynolds number is very small. The operational method is used to obtain exact solutions for the fluid velocity and the shear stress on the plate. Quantitative analysis of the results are presented with a view to disclose the simultaneous effects of the magnetic field and the fluid elasticity on the flow and the wall shear stress for different periods of pulsation of the plate. It is shown that the classical and hydromagnetic Rayleigh solutions are limiting cases of the present analysis.     

热声载荷下高温合金薄壁结构非线性动态响应特性

针对航空航天薄壁结构热声疲劳问题,采用解析法和有限元法相结合,研究矩形薄板样件的非线性动态响应特性。首先,推导了四边简支矩形板在热声载荷下的四阶非线性偏微分大挠度运动方程,并利用伽辽金法将其转化为模态坐标系下的二阶微分方程组;对该方程组进行单自由度简化,计算并分析了平面温度与温度梯度对矩形板振动响应的影响。然后,采用有限元方法计算出四边简支矩形钛合金板在不同温度下的模态频率,以及定常声压级、不同温度下的振动位移和应力响应,并着重对位移功率谱密度进行了详细分析。基于上述计算结果,对响应基频随温度变化关系进行了对比分析,并研究了矩形板屈曲和跳变响应特征。     

含板类柔性附件的充液航天器动力学研究

对含有板类柔性附件和曲壁轴对称充液储腔的复杂航天器系统进行动力学建模和耦合机理研究。首先，采用Kirchhoff-Love薄板理论对航天器的板类柔性附件进行研究，通过D’Alembert原理得到柔性附件的振动方程，运用模态假设法将混合方程转换为常微分方程。其次，通过推导充液航天器储腔内任意点的运动，得到储腔液体的牵连速度势函数，采用Gauss超几何级数得到液体相对速度势函数的解析形式，通过Hamilton变分原理推导液体晃动的运动方程，以及液体速度势函数模态系数的控制方程。最后采用准坐标Lagrange方程得到耦合航天器系统的状态方程，通过数值仿真校验系统动力学模型的有效性。研究结果表明，刚性平台、液体、柔性附件的相互耦合效应使得航天器系统存在复杂动力学行为，在复杂航天器系统动力学建模过程中需要充分考虑液体晃动和柔性附件振动的影响，柔性附件的安装位置对于耦合航天器系统的动力学行为也有着重要影响。     

Motion of deformable planets and stability of their stationary rotations

A mechanical system consisting from N deformable spheres interacting according to the law of gravity is considered as a model of planetary system. Deformations of the viscoelastic spheres are described according to the model of the theory of elasticity of small deformations, the Kelvin-Voigt model of viscous forces, and occur under the action of gravitational fields and fields of centrifugal forces. Approximate equations describing motions of the centers of mass of the spheres and their rotations relative to the centers of mass are constructed by the method of separation of motions on the basis of solving quasistatic problems of the theory of viscoelasticity with allowance made for smallness of sphere deformations. Using the first integral of conservation of the angular momentum of the system relative to its center of mass, the expression for the changed potential energy is obtained with the use of the Routh method. An investigation of stationary rotations is carried out, and it is shown that all of them are unstable, if the number of planets is more than two.     

夹芯的典型参数对夹层板受迫振动影响分析

根据伽辽金法,用Matlab/Simulink软件对推导的经典板假设理论、一阶剪切理论蜂窝夹层板运动方程进行了数值仿真。简单算例的计算结果表明两者基本一致。基于一阶剪切理论讨论了蜂窝夹芯泊松比对蜂窝夹层板低阶频率的影响。发现当泊松比接近1时对频率响应有显著的影响。     

Igniter jet dynamics in solid fuel ramjets

The dynamics of a two dimensional plane jet injected at the base of a step, parallel to the wall, in backward facing step flow geometry is numerically studied. The objective of this work is to gain insight into the dynamics of the igniter flow field in solid fuel ramjet motors. Solid fuel ramjets operate by ingestion of air and subsequent combustion with a solid fuel grain such as polyethylene. The system of governing equations is solved with a finite volume approach using a structured grid in which the AUSM⁺ scheme is used to calculate the convective fluxes. The Spalart and Allmaras turbulence model is used in these simulations. Experimental data have been used to validate the flow solver and turbulence model simulation results. The comparison of the numerical results and experimental data has validated the use of the adopted turbulence model for the study of this type of problem. A special attention is paid to the igniter jet exit location. It is shown that the wall jet igniter, issuing from the base of the step, drastically changes the structure of recirculating region of backward facing step flow and produces large and damaging shear stress on the fuel surface. Moving the igniter jet exit location to the top of the backward facing step changes the flow field favorably, by reducing the fuel surface shear stress by an order of magnitude and maintaining the recirculating region behind the step, which can provide proper residence time for the fuel–air mixture chemical reactions.     

翼身组合弹箭马格努斯效应数值模拟研究

为研究翼身组合弹箭马格努斯特性及产生机理,采用完全时间相关的非定常N-S方程,对带翼弹箭在高速旋转状态下的绕流场进行数值模拟,得到马格努斯力和力矩系数随攻角变化的规律,所得结果与阿诺德工程发展中心（AEDC）试验及陆军研究实验室（ARL）计算结果吻合很好。分析表明压力差是产生马格努斯力的主因,切应力产生的马格努斯力只占压力产生马格努斯力的1%;弹身马格努斯力除α40°外皆为负,舵马格努斯力始终为正;α5°~30°每个舵的马格努斯力不是正弦变化规律,但合力呈现正弦变化规律。     

纤维缠绕封头结构的一般性方程及其解

本文在壳体理论和均衡型网络分析的基础上,建立了纤维缠绕结构封头问题的一般性整化方程,可以用来求解封头曲面形状,纤维缠绕角和壳体厚度、纤维应力和应变、封头位移值、容积及其改变率、纱线长度和滑移系数等。对于等张力封头,给出了解析解;对于平面缠绕封头,用Rung-Kutta方法和Simpson方法给出了数值解,从而实现了表格化。     

Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.     

功能梯度压电材料层状结构中的SH波

基于线性压电弹性理论,利用传递矩阵法,分析了功能梯度压电材料层状结构中的SH波传播特性,研究了压电梯度覆盖层中初始应力对SH波传播的影响。压电覆盖层的材料性能如弹性、压电、介电系数和密度沿厚度方向呈梯度变化。数值分析结果表明,适当的材料梯度分布,可使SH波倾向于沿覆盖层表面传播,由此能够获得更好的机电耦合性能;同时,初始应力使得波传播的相速度减小,但增大了机电耦合系数。文中的分析方法和结论,对固体火箭发动机超声探伤及其压电类传感器的研制和选择有一定的参考意义。     

圆环压力容器均衡缠绕线型设计及稳定性分析

基于网络理论,得到了纤维单螺旋、螺旋加环向均衡型缠绕圆环压力容器的线型方程。应用微分几何理论,给出了同时满足均衡型和稳定缠绕双重条件的线型滑移系数、相对弯曲半径以及两向纤维层厚度比之间的关系。计算结果表明,单螺旋缠绕方式和较大的相对弯曲半径均能提高均衡缠绕线型的稳定性;对于通常研制的圆环压力容器,纤维材料和芯模间的摩擦系数达到0.2~0.3以上,即可实现均衡型缠绕。所提出的环壳均衡缠绕线型和轨迹稳定判别方法,对指导此类产品的缠绕具有重要意义。     

压电层合板壳的数值分析与控制仿真

从虚功方程出发,推导出具有压电传感器和驱动器的层合板壳的机电耦合动力方程,建立了新的压电固体单元以模拟压电层合结构的力学特性和振动控制。通过引入EAS模式,代替通常采用的增加非协调函数的办法克服模拟薄板时所遇到的过高剪切应变能的缺陷,从而明显减少了内部变量的个数,提高了计算效率;进而在厚度方向上增加一个线性分布的横向应变,克服了用于壳体结构的分析时所遇到的厚度自锁问题;提出了一个新的电势插值函数,大大减少了电自由度的个数,显著降低了数据读取、存储和凝聚电自由度的计算花费。数值算例表明,推导的单元适用于薄壳结构的数值分析,并具有很好的对歪斜网格的适应性。     

纤维缠绕圆环压力容器设计分析

基于网格理论,得到了纤维缠绕圆环压力容器在内压作用下的平衡方程。求解方程,得均衡缠绕角和纤维厚度都是平行圆半径R的减函数,即圆环外缘最小;纤维应力是R的增函数,即圆环外缘最大。利用最大应力强度准则,得到了单一螺旋缠绕及螺旋加环向缠绕圆环压力容器爆破压强的计算式。为了使计算的爆破压强与实际结果相符合,纤维发挥强度的选取必须由模拟试验确定。     

固冲发动机补燃室内强迫对流条件下硼颗粒燃烧速率研究

硼颗粒在通过固体火箭冲压发动机的燃气发生器喷管进入补燃室的过程中,颗粒通常都会受到高速气流的作用。此时,静止条件下硼颗粒的燃烧模型不再适应。对强迫对流条件下的硼颗粒燃烧的二维问题建立了数学模型,通过物理、数学简化,将偏微分方程组化为易于求解的常微分方程组,最后得到燃烧速率的显示表达式,并进行了求解,给出了硼颗粒周围边界层内温度场、浓度场及颗粒燃烧速率随雷诺数Re的变化规律。     

碳化材料三维烧蚀热响应有限元计算研究

针对碳化烧蚀热防护材料三维温度场计算问题进行了研究。采用弹簧松弛法模拟防热层表面后退运动,应用化学反应动力学模型描述材料内部热解过程,内部温度场计算模型考虑了防热材料的热传导、热解吸热、热解气体在碳化层内的流动以及热解气体与碳化层之间的热交换。对控制方程采用有限元方法进行离散,时间方向采用Newton-GMRES隐式迭代推进求解。将计算结果与经典程序的计算结果及实验数据进行了比对,初步验证了计算方法的可靠性,并通过球头算例展示了程序对三维问题的良好处理能力。     

Growth and decay of weak discontinuities in radiative gasdynamics

Growth and decay properties of weak discontinuities headed by wave fronts of arbitrary shape in three dimensions are investigated in a thermally radiating inviscid gas flow. The effects of radiative transfer are treated by the use of a general differential approximation for a grey gas of arbitrary opacity including effects of radiative flux, pressure and energy density. The transport equations representing the rate of change of discontinuities in the normal derivatives of the flow variables are obtained, and it is found that the nonlinearity in the governing equations does not contribute anything to the radiation induced waves. In contrast to the radiation induced waves, the nonlinearity in the governing equations plays an important role in the interplay of damping and steepening tendencies of a modified gasdynamic wave. An explicit criterion for the growth and decay of a modified gasdynamic wave along bicharacteristics curve in the characteristic manifold of the governing differential equations is given and the special reference is made of diverging and converging waves. It is shown that there is a special case of a compressive converging wave for which the stabilizing influences of thermal radiation and the wave front curvature are not strong enough to overcome the tendency of the wave to grow into a shock.     

超声速气流下黏弹性夹层壁板非线性颤振分析

基于Kelvin-Voigt黏弹性本构模型、von-Karmen薄板大变形理论和三阶气动力活塞理论建立了三维黏弹性夹层壁板的气动弹性颤振方程。使用Galerkin截断方法,对超声速气流下,四边简支黏弹性夹层壁板颤振的非线性特性进行了研究。对于非线性一阶截断方程,研究了它的平衡点及稳定性随来流速度的变化情况,得到了系统发生静态分叉时的临界速度;对于非线性二阶截断方程,使用数值仿真分析方法,得到了系统发生Hopf分叉时的临界速度,并利用响应、相图等手段研究得到黏弹性夹层板随来流速度变化的动力学特性。