On averaged and normal form equations

The method of ayeraging has long been an important method for the analysis of nonlinear systems. One method using normal forms has more recently become a tool in applied mathematics. Both methods convert systems of ordinary differential equations to simpler equations by using a sequence of change of variables. This study can be interpreted as a local analysis in that it treats equations that are nonlinear perturbations of linear equations. We show that the two methods are essentially equivalent.This work has been supported by the National Science Foundation, Grant No. NSF/MEA 8310966. Deceased.     

一类多自由度强非线性振动系统主共振的渐近解法

提出一种渐近方法用来处理一类多自由度强非线性自治振动系统，它是新渐近方法￣［１］的推广。本方法适用于主共振情形，我们建立了振幅和相位所满足的方程。文末用两个例子说明本方法的有效性。     

梁的动力稳定性分析的有限元方法

提出了对梁进行动力学稳定性分析的有限元方法──给出了单元质量矩阵，抗弯刚度矩阵，几何刚度矩阵及相应的Ｍａｔｈｉｅｕ方程，通过坐标变换消除了方程的动力与静力耦合，然后说明了由这种具有参数激励耦合的多自由度系统的Ｍａｔｈｉｅｕ方程求得系统一般参数共振及组合参数共振的过渡曲线的约束参数方法与多尺度方法。最后作为算例求出了均匀简支梁受简谐轴向力作用时的过渡曲线。     

侧柱对串列双柱脉动压力的干扰

研究了串列双圆柱旁加上一个等直径的圆柱，组成一个等边三角形排列的三圆柱的脉动压力分布．着重研究侧柱对串列双圆柱脉动压力分布的影响．研究的结果表明，绕流等边三角形排列的三圆柱，受影响最严重的是后柱．脉动压力分布出现了严重的不对称，外侧的压力脉动极其强烈，内侧的压力脉动较弱，与时均压力分布，很好的对应关系．另外，侧柱对于串列双圆柱是否达到超过临界间距的绕流流态，有很大的影响     

多孔饱和半空间上刚体垂直振动的轴对称混合边值问题

研究圆柱形刚体在多孔饱和半空间上的垂直振动．首先应用Ｈａｎｋｅｌ变换求解多孔饱和固体的动力基本方程———Ｂｉｏｔ波动方程．然后按混合边值条件建立多孔饱和半空间上刚体垂直振动的对偶积分方程，用Ａｂｅｌ变换化对偶积分方程为第二类Ｆｒｅｄｈｏｌｍ积分方程．文末给出了多孔饱和半空间表面动力柔度系数的计算曲线．     

Shock waves from an open-ended shock tube with different shapes

A new method for decreasing the attenuation of a shock wave emerging from an open-ended shock tube exit into a large free space has been developed to improve the shock wave technique for cleaning deposits on the surfaces in industrial equipments by changing the tube exit geometry. Three tube exits (the simple tube exit, a tube exit with ring and a coaxial tube exit) were used to study the propagation processes of the shock waves. The detailed flow features were experimentally investigated by use of a two-dimensional color schlieren method and by pressure measurements. By comparing the results for different tube exits, it is shown that the expansion of the shock waves near the mouth can be restricted by using the tube exit with ring or the coaxial tube exit. Thus, the attenuation of the shock waves is reduced. The time histories of overpressure have illustrated that the best results are obtained for the coaxial tube exit. But the pressure signals for the tube exit with ring showed comparable results with the advantage of a relatively simple geometry. The flow structures of diffracting shock waves have also been simulated by using an upwind finite volume scheme based on a high order extension of Godunov's method as well as an adaptive unstructured triangular mesh refinement/unrefinement algorithm. The numberical results agree remarkably with the experimental ones.     

Modeling of in-situ biorestoration of organic compounds in groundwater

A convergent numerical method for modeling in situ biorestoration of contaminated groundwater is outlined. This method treats systems of transport-biodegradation equations by operator splitting in time. Transport is approximated by a finite element modified method of characteristics. The biodegradation terms are split from the transport terms and treated as a system of ordinary differential equations. Numerical results for vertical cross-sectional flow are presented. The effects of variable hydraulic conductivity and variable linear adsorption are studied.     

部分相干像面散斑技术

本文以光的部分相干性理论为指导,讨论了部分相干像面散斑(通常称为白光散斑)技术的关键.其结果可与激光像面散斑媲美.     

Monodromy and nonintegrability in complex Hamiltonian systems

This paper investigates the monodromy representation of the normal variational equation along a phase curve of a two-dimensional complex analytic Hamiltonian system. Geometrical conditions are presented which guarantee reducibility, together with additional hypotheses to ensure complete reducibility. Symmetries in the equations are treated in detail. Applications to establishing the nonintegrability of specific systems are presented.     

Thermal expansivity of particulate composites: Interlayer versus molecular model

We continue the comparison of the results of an interlayer model, based on the theory of elastic continua, and a molecular model, derived from a theory of mixtures, previously presented in terms of bulk moduli K. We now derive expressions for the dependence of the thermal expansivity _c on the volume fraction _f of the filler, at low and elevated values of _f . Correspondencies between the characteristic parameters, viz. adhesion and repulsion ratios on the one hand, and interlayer content and thermal properties of matrix, filler, and layer, on the other, are examined. Since in the molecular theory both andK are derived from an equation of state, the identical set of parameters determines both functions and suggests correlations between them.