Multi-symplectic method for generalized Boussinesq equation

The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations （PDEs） derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations.     

Critical velocity of sandwich cylindrical shell under moving internal pressure

Critical velocity of an infinite long sandwich shell under moving internal pressure is studied using the sandwich shell theory and elastodynamics theory. Propagation of axisymmetric free harmonic waves in the sandwich shell is studied using the sandwich shell theory by considering compressibility and transverse shear deformation of the core, and transverse shear deformation of face sheets. Based on the elastodynamics theory, displacement components expanded by Legendre polynomials, and position-dependent elastic constants and densities are introduced into the equations of motion. Critical velocity is the minimum phase velocity on the desperation relation curve obtained by using the two methods. Numerical examples and the finite element （FE） simulations are presented. The results show that the two critical velocities agree well with each other, and two desperation relation curves agree well with each other when the wave number k is relatively small. However, two limit phase velocities approach to the shear wave velocities of the face sheet and the core respectively when k limits to infinite. The two methods are efficient in the investigation of wave propagation in a sandwich cylindrical shell when k is relatively small. The critical velocity predicted in the FE simulations agrees with theoretical prediction.     

空间刚柔性机械臂振动的精细控制

本文在双连杆空间柔性机械臂系统非线性动力学方程的基础上,运用线性二次型（LQ）最优控制方法讨论了机械臂消除残余振动的控制问题。本文重点在于系统计算过程中,放弃了传统的差分类算法,对时变控制系统,引入时程精细积分方法,由于精细积分方法在有限的时间步长内又进行了更精细的划分,同时避免了差分法的许多计算障碍,使得该计算方法具有计算精度高及数值计算无条件稳定等特点。文中针对双连杆空间柔性机械臂系统这一典型结构,给出了其精细控制律,以说明精细积分法的优越性。     

Preparation and UV-light Absorption Property of Oleic Acid Surface Modified ZnO Nanoparticles

Syntheses of zince oxide(ZnO) nanoparticles by direct precipitation and surface modification with oleic acid were reported. ZnO nanoparticles were characterized via X-ray diffractometry(XRD), transmission electron microscopy(TEM), infrared spectroscopy(IR) and UV-Vis spectroscopy. The prepared ZnO nanoparticles were nearly spherical and highly crystalline with an average size of 29 nm. In addition, high UV-light absorption properties of oleic acid surface modified ZnO nanoparticles were successfully obtaine...     

NUMERICAL METHOD BASED ON HAMILTON SYSTEM AND SYMPLECTIC ALGORITHM TO DIFFERENTIAL GAMES

The resolution of differential games often concerns the difficult problem of two points border value (TPBV), then ascribe linear quadratic differential game to Hamilton system. To Hamilton system, the algorithm of symplectic geometry has the merits of being able to copy the dynamic structure of Hamilton system and keep the measure of phase plane. From the viewpoint of Hamilton system, the symplectic characters of linear quadratic differential game were probed; as a try, Symplectic-Runge-Kutta algorithm was presented for the resolution of infinite horizon linear quadratic differential game. An example of numerical calculation was given, and the result can illuminate the feasibility of this method. At the same time, it embodies the fine conservation characteristics of symplectic algorithm to system energy.     

基于含苯硼酸三嵌段共聚物的糖响应性水凝胶

设计合成了一类新型结构的聚环氧乙烷(PEO)大分子链转移剂,调控3-丙烯酰胺基苯硼酸(AAPBA)的可逆加成断裂-链转移(RAFT)自由基聚合,合成得到3种PAAPBA链段长度不同的PAAPBA-bPEO-b-PAABPA3嵌段共聚物.研究了3种聚合物在生理pH值下的凝胶化行为,证明凝胶的形成与PAABPA的长度有关,当该链段较长时,由于PAABPA链段疏水性太强,不能形成稳定的水凝胶.详细研究了聚合物浓度、温度、葡萄糖浓度对凝胶流变行为的影响,证明共聚物浓度越高,形成的凝胶的强度更大,性质上更接近于固体,浓度较高条件下形成的凝胶的转变温度较高.凝胶表现出葡萄糖敏感性,当高葡萄糖存在时,随时间延长,凝胶会发生崩解直至最后溶解.凝胶亲水微区能包载蛋白质FITC-BSA,加入葡萄糖后,FITC-BSA的释放加快.     

序列可控聚合

序列可控聚合是高分子合成方法学的"圣杯",是控制高分子精密结构,进而实现高级功能的重要前提。其最终目标是建立精确控制聚合物单体序列的新方法,深入揭示聚合物结构与性能的关系,从本质上理解单个高分子链内及高分子链间的相互作用,实现单个或几个高分子链的可控链折叠和精密自组装,发展新型功能材料。本文从生物大分子、模板聚合、固相合成、链式聚合以及逐步聚合等方面总结了相关的研究进展,并且就开发精密、高效的序列可控聚合方法以及如何体现序列结构对材料性能的重要影响进行了展望。     

线性Hamilton系统边值问题的保辛数值方法

以Hamilton系统的正则变换和生成函数为基础研究线性时变Hamilton系统边值问题的保辛数值求解算法.根据第二类生成函数系数矩阵与状态传递矩阵的关系,构造了生成函数系数矩阵的区段合并递推算法,并进一步将递推算法推广到线性非齐次边值问题中;然后利用生成函数的性质将边值问题转化为初值问题,最后采用初值问题的保辛算法求解以达到整个Hamilton系统保辛的目的.数值算例表明该方法能够有效地求解线性齐次与非齐次问题,并能很好地保持Hamilton系统的固有特性.     

连续时间线性约束LQ控制问题的时程精细积分方法

本文基于连续时间线性约束LQ控制问题,给出时段的消元公式。由于消元过程与消元次序无关,故可在此过程中引入2N类高精度时程积分方法,求出Riccati方程后,对状态向量进一步采用时程精细积分法,可确定系统非常精确的状态向量,该方法不仅保证了系统的计算精度,而且有很好的数值稳定性,数值例题说明了本文方法的有效性。     

桥梁结构移动平稳随机荷载识别新方法

移动的平稳随机荷载对简支梁的作用,相当于固定的调制函数已知的非平稳随机荷载对简支梁结构的作用.本文以此为基础,研究了移动平稳随机荷载的识别问题.首先基于虚拟激励法的思想,利用特征值分解及奇异值分解技术,由虚拟位移响应反演虚拟广义坐标,有效地避免了矩阵求逆,得到高精度的广义坐标谱;同时利用Wiener-Khintchine关系及Duhamel积分,由广义坐标谱值反演得到平稳随机激励谱密度.仿真算例表明,只要适当地选取参振振型及测点位置,本文方法可以有效地识别桥梁结构的移动平稳随机荷载.