具有非线性热源项的耦合杆系统

主要以经典的算子半群理论为依据,研究了一类具有非线性热效应的耦合杆系统的长时间行为.首先在齐次边界条件和初始条件下,证明了系统解的存在唯一性;其次通过渐近先验估计,证明了系统有界吸收集的存在性;最后利用算子半群的分解技巧,得到了系统全局吸引子的存在性.     

刚棒线团分子的自组装研究进展

超分子化学领域的自组装研究是近年来研究的热点,对这种由一种或多种结构单元自发聚集而成具有一定尺寸和结构的过程研究已经取得了重大进展。以亲水基团和亲脂基团为主要构成单元的两亲性分子在自组装领域中的表现优异于其他分子,其亲水的刚性棒状基团和疏水的柔性线团基团通过不同方法共同构成了各种类型的刚柔两亲性分子,而在水溶液中自组装而成不同结构与性能的聚集体又与两亲性分子的结构密切相关。目前,已报道的调控超分子自组装的方法大致可以分为两类,即外部刺激法和自身修复法,本文亦从这两个方面总结了近年来刚棒-线团分子自组装的研究进展。     

Flexural-torsional bifurcations of a cantilever beam under potential and circulatory forces I: Non-linear model and stability analysis

The stability of a cantilever elastic beam with rectangular cross-section under the action of a follower tangential force and a bending conservative couple at the free end is analyzed. The beam is herein modeled as a non-linear Cosserat rod model. Non-linear, partial integro-differential equations of motion are derived expanded up to cubic terms in the transversal displacement and torsional angle of the beam. The linear stability of the trivial equilibrium is studied, revealing the existence of buckling, flutter and double-zero critical points. Interaction between conservative and non-conservative loads with respect to the stability problem is discussed. The critical spectral properties are derived and the corresponding critical eigenspace is evaluated.     

螺旋细杆的均匀扭转振动

讨论螺旋细杆的特殊形式扭转振动，即均匀扭转振动．以非圆截面杆和有原始曲率的圆截面杆为研究对象．杆作均匀扭转振动时各截面有相同的扭角变化规律，且杆中心线的几何形状不受振动过程的影响．研究表明，扭振来源于杆截面的非对称性及杆的原始曲率．杆的扭振规律与单摆运动相似，其动力学方程存在精确解．圆环杆的均匀扭振为螺旋杆的倾角为零时的特例．     

炭纤维增强环氧树脂复合材料/N80钢摩擦学性能研究

利用MG-200型摩擦磨损试验机研究了炭纤维增强环氧树脂复合材料/N80钢的摩擦学性能,考察了介质温度对摩擦学性能的影响;用扫描电子显微镜分析了磨损表面形貌.结果表明:在干摩擦条件下,炭纤维增强环氧树脂复合材料与N80钢对摩时的摩擦系数较低,炭纤维增强环氧树脂复合材料的磨损主要表现为树脂基体脱落碳化和炭纤维的折断剥落,偶件钢环则呈现明显的磨粒磨损特征;在油井产出液润滑下炭纤维增强环氧树脂复合材料的磨损率较低,摩擦系数和磨损率随着润滑介质温度的升高而增大,偶件钢环则呈现明显的磨粒磨损和腐蚀磨损特征.     

Patterned growth of zinc oxide nanorods using poly(vinyl alcohol)-N-methyl-4(4′-formylstyryl)pyridinium methosulfate acetal and zinc acetate mixture as a seed layer

This paper reports a new method for fabricating two-dimensional ZnO nanorod patterns. A water soluble mixture of poly(vinyl alcohol)-N-methyl-4(4′-formylstyryl)pyridinium methosulfate acetal (PVA-Sbq) and zinc acetate (ZnA) was used as a negative photoresist to produce the desired patterns using conventional photolithography. Hydrothermally-grown ZnO nanorods were grown selectively on the calcined PVA-Sbq/ZnA patterns. The appropriate concentration of PVA-Sbq and ZnA that can produce the desirable seed layer pattern was determined experimentally. Furthermore, the effects of the calcination time on the morphology and vertical alignment of ZnO nanorods were investigated. The vertically-aligned ZnO nanorods were generated by sufficient calcination of the patterned seed layer. On the other hand, the aspect ratio of ZnO nanorods decreased slightly with increasing calcination time. This new approach provides a simple and cost-effective method for fabricating ZnO nanorod patterns which can be beneficial in various solid-state devices and optoelectronic applications.     

连接阻尼对弹性杆纵向碰撞响应的影响

分析了刚度和阻尼并存的一般边界条件下线弹性杆与刚体的纵向碰撞过程,得到了碰撞后第一个波动周期杆振动的位移、速度和应力的解析表达式,讨论了碰撞持续时间为2倍杆长与波速比的条件.将导出的解析表达式通过具体的算例代入计算,讨论了不同质量比、不同连接刚度条件下连接阻尼对于碰撞过程中杆中质点速度及应力响应的影响.研究表明,连接阻尼改变了受碰撞弹性杆的振动模式,连接阻尼影响着碰撞反射波速度和应力的突变幅度;连接阻尼增大,杆中速度和应力响应分布变平缓:在连接刚度较大的情况下,连接阻尼变化对于杆中质点速度和应力影响较大;碰撞持续时间与质量比、连接刚度、连接阻尼及杆长有关,与碰撞的初速度无关;在质量比较大的情况下,连接阻尼使得反射波到达杆碰撞端时,杆端的应力有显著的变化.     

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.     

用升降法求95连杆疲劳极限的探讨

为了较精确地求出95连杆的疲劳极限,本文将在材料疲劳试验中应用较广的升降法推广应用于连杆,给出了用升降法求构件疲劳极限的基本过程。文中首先选取了试验的控制因素并确定了连杆的控制点(应力被选定为控制应力的点定义为控制点)。然后在四级应力水平下进行了连杆的疲劳试验,并以最大应力幅点的应力为计算应力求出了连杆的疲劳极限。     

Justification of the kinematic assumptions for thin-walled rods with shallow profile

In this Note we present a justification of the kinematic assumptions for thin-walled rods with shallow profile. These assumptions are fundamental to writing the one-dimensional equilibrium equations for such structures. The obtained kinematics are different from the Vlassov case, which is only valid for strongly curved profiles. They are also different from the that classically used in shell theory. The justification given in this Note is based on an asymptotic approach. To cite this article: L. Grillet et al., C. R. Mecanique 333 (2005).