基于传递函数法的大展弦比机翼阵风响应分析

将传递函数法应用于大展弦比机翼的阵风响应分析。首先,基于二元机翼的运动方程和准定常片条理论建立机翼的阵风响应微分方程,对其进行Laplace变换,并转换为状态空间方程形式。然后,运用传递函数方法,获得机翼响应在频域的解析解,通过Laplace数值逆变换求得机翼在时域内的响应。通过与已有文献结果对比,验证了本文方法的正确性。最后,采用该方法求解了\"1-cos\"型阵风和连续大气湍流作用下的机翼响应,并对结果进行了分析讨论。     

A discrete algorithm for complex frequency-domain convolutions

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弹性机翼阵风响应数值计算方法

建立了求解弹性机翼阵风响应的计算方法.在计算中,通过采用数值方法求解三维非定常Euler方程来获得气动特性;采用模态叠加的方法考虑弹性影响,实现了流体力学和弹性力学的耦合计算.通过对刚性机翼在攻角突然增大的阵风作用下的响应历程计算和二维NLR7301翼型的极限环振荡计算,对计算方法进行了验证.此后在"1-cos"阵风响应的计算中考虑弹性效应影响,先是只考虑了结构变形的前三个基本模态,弹性机翼气动力响应的计算结果与刚性机翼的响应计算结果有比较大的区别,弹性机翼阵风响应的升力峰值低于刚性机翼,这与文献中的结果是一致的.最后在计算中考虑了高阶弹性模态,计算结果表明:考虑高阶模态后,机翼气动力计算结果的总体变化趋势与只考虑前三个模态时基本一致,但结果中出现了高频的波动,波动的频率与高阶模态本身的频率有关.     

基于传递函数法的带多个外挂机翼颤振分析

基于带外挂机翼结构和气动特点，使用带有半解析半数值特性的传递函数方法进行处理．首先，通过机翼的运动微分方程、二元机翼非定常气动力Therdorson 模型、结合外挂挂载处的内力平衡与位移状态条件，得到了三维的带多个外挂大展弦比机翼的颤振微分方程．进而，使用传递函数方法，先将颤振计算方程整理成为状态空间方程形式，结合求解复特征值的方法，完成了带多个外挂大展弦比机翼的动气动弹性稳定性分析．对比已有文献的计算结果以及通过有限元方法进行的仿真结果，证实了文章所提计算方法的准确性和高效性，结合传递函数方法的优势，进一步将文章方法拓展到机翼的固有频率和发散速度求解．文章结尾，分析了外挂数量、外挂质量、转动惯量及位置分布等变量对带多个外挂大展弦比机翼的动气动弹性稳定性的影响．     

坡形加热下的二维广义磁热黏弹性问题研究

运用具有一个热松弛时间的广义热黏弹性理论,研究了处于均布磁场中的二维磁热黏弹 性问题. 运用Laplace变换(对时间变量)和Fourier变换(对于一个空间变量),得到了变 换域内场量的精确表达式,并把结果应用到表面受到坡形加热的半空间问题. 应用 数值逆变换得到了时间-空间域内场量的解,对丙烯酸塑料 给出场量的响应图. 并把运用广义热黏弹性理论所得的结果与传统热黏弹性理 论及热弹性理论下的结果进行了比较.     

基于Fourier级数展开的Laplace数值逆变换

研究了基于Fourier级数展开的Laplace数值逆变换在黏弹性力学问题中的有效应用,这类方法的关键涉及计算参数的选择. 构造了优化模型,对计算参数寻优,以黏弹性层合圆柱薄壳在轴压下的准静态变形以及受突加内压黏弹性圆筒在平面应变条件下的动应力响应为例阐述方法的应用. 结果表明:通过优化模型能有效地确定计算参数;且当反演参数与计算时间的乘积在一定范围内时,Fourier级数展开法均能给出一致的结果,由此,可按与计算时间成反比的关系来确定反演算法中的参数.      

Laplace transform-boundary element coupling method for viscous fluid-structure impact analysis

Based on linearized 2-D Navier-Stokes equation, a Laplace transform-boundary element coupling method for viscous fluid-structure impact analysis is proposed. Under assumption of incompressibility for the fluid, the corresponding equivalent boundary integral equation in terms of the potential function and stream function is first established by Lamb's transform in the Laplace transform domain. It enables us to solve impact water problems in frequency domain by the boundary element method, in which the effect of viscous flow on the dynamic response can be taken into account. Then a complete solution of the problem under consideration in time domain is obtained by means of Durbin's formulas for the numerical inversion of the Laplace transform. Finally, a practical example is given to confirm the validity of the present method. Project supported by the National Defence Foundation of Science & Technology of China (No. J14. 8. 1. JW0515).     

基于拉氏变换的弹性动力学插值型重构核粒子法

插值型重构核粒子法的形函数具有离散点插值特性和不低于核函数的高阶光滑性,因而不仅可以直接施加本质边界条件,同时也保证了较高的计算精度．本文将弹性动力学方程作拉氏变换后,在变换域内用插值型重构核粒子法求解,最后再借助Durbin数值反演方法求得时间域的解．针对典型的弹性动力学问题,给出了插值型重构核粒子法的数值算例,并验证了本文方法的有效性．     

线黏弹性球面发散应力波的频率响应特性

基于线黏弹性球面波Laplace域的理论解, 得到了不同传播距离处粒子速度、粒子位移、应力、应变等力学量的传递函数。以标准线性固体模型为例, 重点讨论了粒子速度频率响应函数的传播特征, 指出随着传播距离的增加, 粒子速度幅频响应函数的高频响应会低于低频响应, 而在理想弹性条件下, 粒子速度幅频响应函数的高频响应一直高于低频响应。以弹性半径为0.025 m的空腔爆炸为例, 采用Laplace数值逆变换方法对粒子速度波形的演化进行了分析, 给出了粒子速度强间断幅值及粒子速度峰值随传播距离变化的衰减规律曲线, 指出黏弹性介质中粒子速度幅值的衰减曲线介于理想弹性介质中粒子速度幅值衰减曲线和黏弹性介质中粒子速度强间断幅值衰减曲线之间。

     

一维流体饱和粘弹性多孔介质层的动力响应

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论,在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下,建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型,利用Laplace变换,求得了原初边值问题在变换空间中的解析解,并利用Laplace逆变换的Crump数值反演方法,得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应,分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明,与不可压流体饱和弹性多孔介质相同,不可压流体饱和粘弹性多孔介质中亦只存在一个纵波,并且固相骨架的粘性对动力行为有显著的影响。     

空间杆系结构非线性动力稳定性分析的一种实用算法

本文对任意空间杆系结构进行非线性动力稳定性分析。     

Summation of fourier series with parameter by Laplace tranforms

In this paper, the theorems concerning the summatio of Fourier series with parameter are given by using the Laplace transforms. By means of the known result of Laplace transforms, many new, important problems of summation of Fourier series with parameter in mechanics can be solved.     

SUMMATION OF FOURIER SERIES WITH PARAMETER BY LAPLACE TRANSFORMS

In this paper,the theorems concerning the summation of Fourier series withparameter are given by using the Laplace transforms.By means of the known result ofLaplace transforms,many new,important problems of summation of Fourier serieswith parameter in mechanics can be solved.     

考虑损伤的粘弹性梁的纯弯曲

根据粘弹性损伤理论,分析了带损伤粘弹性矩形梁在受纯弯曲时损伤对应力的影响,得到了在Laplace变换域内损伤场和应力场的分布.利用Laplace数值逆变换,分别得到了损伤弹性梁和损伤粘弹性梁的最大应力和最大损伤值,分析了材料的粘性对梁内应力和损伤的影响.     

Rotary aerodynamic derivatives in the asymptotic theory of a high-aspect-ratio wing

The linear problem of inviscid incompressible flow around a high-aspect-ratio wing at an angle of attack and in the presence of steady pitching and rolling rotation is considered. The main integral equation of the problem is reduced to a sequence of one-dimensional integral equations without use of the matched asymptotic expansions method. The first few terms of the series for the circulation distribution over the wing surface are calculated. For an elliptic high-aspect-ratio wing the corresponding aerodynamic forces are calculated. The derivatives of the aerodynamic coefficients of the wing with respect to the angle of attack and the angular velocities are determined. The asymptotic expressions obtained are compared with the results of numerical calculations of the corresponding derivatives using the discrete vortex method.     

任意段变模量桩纵向振动的解析解

建立了均质土中考虑桩端土和桩侧土作用的任意段变模量桩,讨论了在桩顶受纵向激励时的定解问题,并用拉氏变换(Laplace)求得桩顶速度频域响应的解析解,然后利用卷积定理和拉氏逆变换求得桩顶速度时域响应的解析解,并将其运用到桩基质量的动力检测中.对弹性模量突变桩以及模量连续变化桩的振动特性作了进一步的研究,并将理论曲线与实测曲线进行了拟合对比,结果表明,两者吻合较好.     

AN ANALYTICAL SOLUTION TO LONGITUDINAL VIBRATION OF A PILE OF ARBITRARY SEGMENTS WITH VARIABLE MODULUS

The vibration problem of a pile of arbitrary segments with variable modulus under exciting force is established, in which the influence of the soil under pile toe and the surroundings is taken into account. With Laplace transforms, the transmit functions for velocity and displacement of pile are derived. Furthermore, in terms of the convolution theorem and inversed Laplace transform, an analytical solution for the time domain response of a pile subjected to a semi-sine impulse is developed, which is the theoretical basis of the sonic method in pile integrity testing. Based on the solution, the vibration properties of pile with sharp or continuous modulus are studied. The validity of this approach is verified through field dynamic tests on some engineering piles. It shows that the theoretical prediction and the response of the pile are in good agreement.     

Contaminant Transport in Fractured Media with Sources in the Porous Domain

We study contaminant flow with sources in a fractured porous mediumconsisting of a single fracture bounded by a porous matrix. In the fracturewe assume convection, decay, surface adsorption to the interface, and lossto the porous matrix; in the porous matrix we include diffusion, decay,adsorption, and contaminant sources. The model leads to a nonhomogeneous,linear parabolic equation in a quarter-space with a differential equationfor an oblique boundary condition. Ultimately, we study the problemu _t = u _yy – u + f(x,y,t),x,y>0, t>0, u _t = –u _x + u _y – u on y = 0; u(0,0,t) =u₀(t), t>0,with zero initial data. Using Laplace transforms we obtain the Green'sfunction for the problem, and we determine how contaminant sources in theporous media are propagated in time.