二维振荡叶栅非定常粘性流动数值模拟

采用显式四步Runge-Kutta格式，结合Baldwon-Lomax紊流模型求解Navier-Stokes方程，借助运动网格技术，完成了对二维振荡叶栅非定常粘性流动的数值模拟。为了加速求解过程，引入了变系数隐式残差光顺方法，取得了较好效果。数值结果与已公布的数据有很好的一致性。     

NORMAL EXPANSION THEORY FOR PENETRATION OF PROJECTILE AGAINST CONCRETE TARGET

Based on the equations which describe the dynamic behavior of material under high-velocity and high-pressure shock, corresponding equations at shock front whose surface is general space curve surface were established. For concrete material, a normal expansion theory was proposed by which some deceleration about time history of the projectile can be analytically given. This normal expansion theory is not only suitable for spherical and cylindrical-nose projectile, but also suitable for other general nose projectile, for example conical nose or ogive-nose. And it is not only suitable for perpendicular shock but also for oblique shock.     

一类振动方程周期解的全局分岔

本文利用Ｍｅｌｎｉｋｏｖ函数方法，通过分析无穷远处轨线的性质，研究一类柱面振动方程周期解的全局分岔问题，获得了第二类闭轨存在性和唯一性的条件。     

Stability and vibration of a helical rod constrained by a cylinder

The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler’s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov’s and Euler’s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form. The project supported by the National Natural Science Foundation of China (10472067). The English text was polished by Yunming Chen.     

振动翼型和襟翼的绕流特性研究

用数值模拟手段详细地研究了振动翼型和襟翼的绕流问题,数值模拟的出发方程为Euler和N-S方程,格式为Bcam-Warming格式的改进型。数值实验主要针对流场的二大特性进行的,即振动对激波的影响和振动对分离的抑制作用,结果表明:(1)随翼型或襟翼的振动激波强度和位置也相应地变化但这一变化滞后于攻角的变化;(2)振幅加大激波强度的变化和激波运动范围也加大;(3)振动频率越高对激波的影响反而较低频时要小;(4)流动条件的不同可使升力回线的走向发生变化;(5)振动对分离有明显的抑制作用。     

具有非线性复刚度的复阻尼振动系统的摄动解

本文首次用摄动法获得了具有非线性复刚度的复阻尼振动系统的自由振动和强迫振动的解，并对这类问题作出了较为详尽的讨论，计算结果与试验结果几乎一致。     

DYNAMICAL FORMATION OF CAVITY FOR COMPOSED THERMAL HYPERELASTIC SPHERES IN NONUNIFORM TEMPERATURE FIELDS

Dynamical formation and growth of cavity in a sphere composed of two incompressible thermal-hyperelastic Gent-Thomas materials were discussed under the case of a non-uniform temperature field and the surface dead loading. The mathematical model was first presented based on the dynamical theory of finite deformations. An exact differential relation between the void radius and surface load was obtained by using the variable transformation method. By numerical computation, critical loads and cavitation growth curves were obtained for different temperatures. The influence of the temperature and material parameters of the composed sphere on the void formation and growth was considered and compared with those for static analysis. The results show that the cavity occurs suddenly with a finite radius and its evolvement with time displays a non-linear periodic vibration and that the critical load decreases with the increase of temperature and also the dynamical critical load is lower than the static critical load under the same conditions.     

随机连续杆纵向振动系统的频率可靠性分析

根据随机连续杆纵向振动系统的固有频率与激振频率差的绝对值不超过规定值的关系准则，定义了随机连续杆纵向振动系统的可靠性模式和系统的可靠度，提出了避免共振的频率可靠性分析方法，对随机连续系统共振问题的准失效分析方法进行了探索。     

斜拉桥拉索的风（雨）激振及控制

目前，国内建造了大量的斜拉桥。随着斜拉桥跨度的增大，拉索的风致振动及风雨激振问题越来越突出。本文总结了国际上的有关研究，特别是拉索风雨激振及控制研究的成果，提出了这一领域中有重要意义的研究方向。     

阶梯式矩形板的振动

用奇异函数建立阶梯式矩形板自由振动和强迫振动的微分方程并求得其通解，用Ｗ算子给出振型函数的表达式及常见支承条件下板的频率方程，本文解可用于多种边界条件的板。