单自由度非线性随机参数振动系统的可靠性灵敏度分析

较好地解决了单自由度非线性随机参数振动系统的可靠性灵敏度问题，应用四阶矩技术和Edgeworth级数把未知的响应和状态函数的概率分布展开成标准的正态分布的表达式，进而确定了系统的可靠度和可靠性灵敏度，并放松了随机参数的分布概型和激励类型。     

分析弹性支承输流管道的失稳临界流速

研究了两端弹性支承输流管道静态失稳和动态失稳临界流速. 根据梁模型横向弯曲振动模态 函数，由两端弹性支承的边界条件得到了其模态函数的一般表达式. 根据特征方程具体分析 了弹性支承刚度、质量比、流体压力和管截面轴向力等主要参数对失稳临界流速的影响. 数 值计算结果表明，管道在弹性支承下的动力稳定性比较复杂，在较小的弹性支承刚度和较小 的参数范围内，管道主要表现为动态颤振失稳；在较大的弹性支承刚度和较大的参数作用下， 管道的失稳形式主要表现为静态失稳；并且失稳临界流速随流体压力和管截面轴向压力的增 加而下降，随管截面轴向拉力的增加而上升.     

1/3 PURE SUB-HARMONIC SOLUTION AND FRACTAL CHARACTERISTIC OF TRANSIENT PROCESS FOR DUFFING''''S EQUATION

The 1/3 sub-harmonic solution for the Buffing's with damping equation was investigated by using the methods of harmonic balance and numerical integration. The assumed solution is introduced, and the domain of sub-harmonic frequencies was found. The asymptotical stability of the subharmonic resonances and the sensitivity of the amplitude responses to the variation of damping coefficient were examined. Then, the subharmonic resonances were analyzed by using the techniques from the general fractal theory. The analysis indicates that the sensitive dimensions of the system time-field responses show sensitivity to the conditions of changed initial perturbation, changed damping coefficient or the amplitude of excitation, thus the sensitive dimension can clearly describe the characteristic of the transient process of the subharmonic resonances.     

A new type of global bifurcation in Hénon map

A simple branch of solution on a bifurcation diagram, which begins at static bifurcation and ends at boundary crisis (or interior crisis in a periodic window), is generally a period-doubling cascade. A domain of solution in parameter space, enclosed by curves of static bifurcation and that of boundary crisis (or the interior of a periodic window), is the trace of branches of solution. A P-n branch of solution refers to the one starting from a period-n (n≥1) solution, and the corresponding domain in parameter space is named the P-n domain of solution. Because of the co-existence of attractors, there may be several branches within one interval on a bifurcation diagram, and different domains of solution may overlap each other in some areas of the parameter space. A complex phenomenon, concerned both with the co-existence of attractors and the crises of chaotic attractors, was observed in the course of constructing domains of steady state solutions of the Hénon map in parameter space by numerical methods. A narrow domain of period-m solutions firstly co-exists with (lies on) a big period-n (m≥3n) domain. Then it enters the chaotic area of the big domain and becomes period-m windows. The co-existence of attractors disappears and is called the landing phenomenon. There is an interaction between the two domains in the course of landing: the chaotic area in the big domain is enlarged, and there is a crisis step near the landing area.     

智能结构密频系统振动控制及其摄动分析

提出一种智能结构密频控制规律的设计方法。其主要工作为：将密频子空间转化为重频子空间,把密频系统作为重频系统上的摄动;为了解决重频密频子空间相对应的特征向量选取的敏感性问题,通过摄动分析得到与重频密频子空间相对应特征向量的线性组合并利用闭环系统特征值极点配置的方法得到重频密频系统的振动规律;把所设计的振动控制规律作用于原系统和摄动系统上,讨论了结构参数改变后对系统的动态特性的影响;最后通过算例证明该方法的有效性。     

Synchronisation and general dynamic symmetry of a vibrating system with two exciters rotating in opposite directions

We derive the non-dimensional coupling equation of two exciters,including inertia coupling,stiffness coupling and load coupling.The concept of general dynamic symmetry is proposed to physically explain the synchronisation of the two exciters,which stems from the load coupling that produces the torque of general dynamic symmetry to force the phase difference between the two exciters close to the angle of general dynamic symmetry.The condition of implementing synchronisation is that the torque of general dynamic symmetry is greater than the asymmetric torque of the two motors.A general Lyapunov function is constructed to derive the stability condition of synchronisation that the non-dimensional inertia coupling matrix is positive definite and all its elements are positive.Numeric results show that the structure of the vibrating system can guarantee the stability of synchronisation of the two exciters,and that the greater the distances between the installation positions of the two exciters and the mass centre of the vibrating system are,the stronger the ability of general dynamic symmetry is.     

含压电材料智能结构动态特性的研究

本文推导了含压电材料智能结构有限元动力方程,讨论了智能结构系统的动态特性,得到了模态形状和相应的模态电压以及考察了具有分布的压电传感器和执行器的四边简支方板的各阶固有频率随以馈增益的变化规律,这些结果将在智能结构控制的优化设计中起到了很大的作用。     

随机结构系统的一般实矩阵特征值问题的概率分析

由于工程实际结构的复杂性和所用材料在统计上的离散性以及测量、加工、制造误差的存在，必然导致具有随机参数的随机结构振动系统，按结构参数的性质来划分，随机振动问题包括两方面内容：(1)确定结构问题；(2)随机结构问题。本文以现代数学理论为依托，研究了随机结构系统的一般实矩阵的特征值问题。根据Kronecker代数、向量值和矩阵值函数的灵敏度分析、一般二阶矩法和概率摄动技术给出了计算随机结构系统的一般实矩阵的特征值和特征向量的数值方法，可以有效地得出随机结构系统的一般实矩阵的特征向量的统计量，发展了2D矩阵值函数的随机结构系统的特征值问题概率分析理论。     

含慢变参数的非线性振动系统的振动特性

慢变参数的振动系统一类典型的非线性系统，工程上的许多振动都于这一类，由于慢变系统的质量、刚度、干扰力等参数是随机时间缓慢的，另一般的参变系统有本质的不同，因此需根据咖以研究。本文讨论了慢变系统的分析方法。同时结合提升机罐笼与钢丝强组成的系统和慢变刚度的转子系统对自汉的和非自治的慢变系统的的夺动特性进行了研究，提出育夺区时的振幅的具体方法。