三维不可压缩Boussinesq-MHD系统解的衰减估计

使用一般能量法研究三维不可压缩Boussinesq-MHD系统在全空间R³中的衰减估计.首先，通过先验估计得到方程组解的高阶空间导数的能量不等式.其次，利用齐次Sobolev空间的范数估计解的有界性.最后，得到与时间有关的方程组解的高阶空间导数最优衰减率.     

Compressible navier-stokes-poisson equations

This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and the optimal decay rates for both unipolar and bipolar compressible Navier-Stokes-Poisson equations are discussed.     

隧道壁湿润引起电磁波衰减率变化的研究

矿井隧道壁湿润会引起电参数改变，从而使电磁波传播衰减率发生变化。当频率略高于隧道截止频率时利用微扰法可知：不论是矩形隧道还是圆形隧道，隧道壁潮湿使电磁波的衰减率降低。当频率远高于截止频率时，利用传统公式法可知：矩形隧道中隧道壁湿润引起衰减增大；圆形隧道中E模式衰减率因电容率的增大而减小，其它各模式则因电容率的增大而增大。     

Asymptotic Behaviors of the Solutions to Scalar Viscous Conservation Laws on Bounded Interval

Abstract This paper concerns the asymptotic behaviors of the solutions to the initial-boundary value prob-lem for scalar viscous conservations laws u_t+f(u)_x=u_(xx) on[0,1],with the boundary condition u(0,t) =u_,u(1,t)=u_+ and the initial data u(x,0)=u_0(x,0)=u_0(x),where u_≠u_+ and f is a given function satisfyingf'(u)>0 for u under consideration.By means of energy estimates method and under some more regular condi-tions on the initial data,both the global existence and the asymptotic behavior are obtained.When u_u_+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shockwaves,which means that │u_-u_+│is small.Moreover,exponential decay rates are both given.     

转捩中平均流剖面对扰动波演化的影响

对槽道流的常规转捩直接数值模拟发现，在转捩“breakdown”即将发生时，除个别T-S波以外，流场中较大幅值的波都已经停止增长；在转捩“breakdown”发生前到发生过程中的短时间内，非线性作用没有明显变化的情况下，典型未增长起来的波的实际增长率却增加了2个数量级以上．分析表明，平均流剖面稳定性改变使非线性作用的支持相对于衰减率有了明显的优势，于是流场中占大多数的长期受衰减率抑制的未增长起来的波能够急速增长，导致转捩的“breakdown”过程迅速完成．     

具有多个时滞的非线性不确定系统的鲁棒稳定和镇定

应用Lyapunov稳定性理论,讨论了一类给出范数扰动界的具有多个时滞的不确定非线性系统的鲁棒稳定性和稳定衰减率,给出了该系统鲁棒稳定的充分条件和具有确定衰减率的稳定条件。同时讨论了一类具有多个时滞的非线性控制系统鲁棒镇定的充分条件,本文给出的结论推广和改进了前人一系列结论。文末,给出了说明该文结论优越性的一个示例并与前人的结论作了比较。     

Numerical analysis of delamination growth for stiffened composite laminated plates

A study of postbuckling and delamination propagation behavior in delaminated stiffened composite plates was presented. A methodology was proposed for simulating the multi-failure responses, such as initial and postbuckling, delamination onset and propagation, etc. A finite element analysis was conducted on the basis of the Mindlin first order shear effect theory and the von-K6rm~n nonlinear deformation assumption. The total energy release rate used as the criteria of delamination growth was estimated with virtual crack closure technique (VCCT). A self-adaptive grid moving technology was adopted to model the delamination growth process. Moreover, the contact effect along delamination front was also considered during the numerical simulation process. By some numerical examples, the influence of distribution and location of stiffener, configuration and size of the delamination, boundary condition and contact effect upon the delamination growth behavior of the stiffened composite plates were investigated. The method and numerical conclusion provided should be of great value to engineers dealing with composite structures.     

An approximation of the first passage probability of systems under nonstationary random excitation

An approximate method is presented for obtaining analytical solutions for the conditional first passage probability of systems under modulated white noise excitation. As the method is based on VanMarcke＇s approximation, with normalization of the response introduced, the expected decay rates can be evaluated from the second-moment statistics instead of the correlation functions or spectrum density functions of the response of considered structures. Explicit solutions to the second-moment statistics of the response are given. Accuracy, efficiency and usage of the proposed method are demonstrated by the first passage analysis of single-degree-of-freedom （SDOF） linear systems under two special types of modulated white noise excitations.     

非线性轴承转子系统稳定性准则的研究

目前对于非线性轴承转子系统，仍普遍采用其线性化系统的对数衰减率作为系统的稳定性判据，这造成了理论和实验结果相差较大。本文对［１］中提出的ＰＣＭ法作了改进，通过对无限长滑动轴承支承对称刚性单盘转子系统的非线性稳定性规律进行的分析，揭示了上述现象的非线性本质，为建立更适用于非线性轴承转子系统的稳定性准则提供参考。     

TRANSIENT RESPONSE OF COPLANAR INTERFACIAL CRACKS BETWEEN TWO DISSIMILAR PIEZOELECTRIC STRIPS UNDER ANTI-PLANE MECHANICAL AND IN-PLANE ELECTRICAL IMPACTS

The dynamic response of multiple coplanar interface cracks between two dissimilar piezoelectric strips subjected to mechanical and electrical impacts is investigated. Solutions to two kinds of electric boundary conditions on crack surfaces, i.e. electric impermeable and electric permeable, are obtained. Laplace and Fourier transforms and dislocation density functions are employed to reduce the mixed boundary value problem to Cauchy singular integral equations,which can be solved numerically. The effects of electrical load, geometry criterion of piezoelectric strips, relative location of cracks and material properties on the dynamic energy release rate are examined.