旋转输液管动力稳定性理论分析北大核心CSCD

基于Lagrange原理和假设模态法建立了旋转输液管的动力学模型.通过降阶升维的方法求解系统的特征值问题,并分析了旋转输液管自由振动特性.得到了不同端部集中质量和转速下,系统特征值随流速升高的演变轨迹.揭示了临界流速随系统参数的变化规律.研究发现,内部流体的流动对旋转输液管动力学特性存在显著影响.在某些参数组合下,系统低阶模态能够形成不同形式的内共振关系.预示了旋转输液管模型蕴含丰富的动力学现象.     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Standard pseudo-Hermitian structure on manifolds and seifert fibration

A strictly pseudoconvex pseudo-Hermitian manifoldM admits a canonical Lorentz metric as well as a canonical Riemannian metric. Using these metrics, we can define a curvaturelike function onM. AsM supports a contact form, there exists a characteristic vector field dual to the contact structure. If induces a local one-parameter group ofCR transformations, then a strictly pseudoconvex pseudo-Hermitian manifoldM is said to be a standard pseudo-Hermitian manifold. We study topological and geometric properties of standard pseudo-Hermitian manifolds of positive curvature or of nonpositive curvature . By the definition, standard pseudo-Hermitian manifolds are calledK-contact manifolds by Sasaki. In particular, standard pseudo-Hermitian manifolds of constant curvature turn out to be Sasakian space forms. It is well known that a conformally flat manifold contains a class of Riemannian manifolds of constant curvature. A sphericalCR manifold is aCR manifold whose Chern-Moser curvature form vanishes (equivalently, Weyl pseudo-conformal curvature tensor vanishes). In contrast, it is emphasized that a sphericalCR manifold contains a class of standard pseudo-Hermitian manifolds of constant curvature (i.e., Sasakian space forms). We shall classify those compact Sasakian space forms. When 0, standard pseudo-Hermitian closed aspherical manifolds are shown to be Seifert fiber spaces. We consider a deformation of standard pseudo-Hermitian structure preserving a sphericalCR structure.Dedicated to Professor Sasao Seiya for his sixtieth birthday     

Exact quantum mechanical vibration-rotation kinetic energy operator of four-particle system in various coordinates

The vibration-rotational kinetic energy operators of four-particle system in various coordinates are derived using a new and simple angular momentum method. The operators are respectively suitable for studying the systems described by scattering coordinate, valence coordinate, Radau coordinate, Radau/Jacobi and Jacobi/valence hybrid coordinates and so on. Certain properties of these operators and their possible applications are discussed.     

在"高聚物的结构与性能"课程中应该引入的几个新概念

在“高聚物的结构与性能”课程教学中，很有必要向学生介绍高分子科学近十几年来的发展，尤其是在高分子凝聚态基本物理问题上的研究成果以及相关的新概念、新知识，特别是我国学者的贡献。本文较为详细地讨论了近年来作者在教学中介绍的几个新概念，如：动态接触浓度、单链凝聚态、凝聚缠结等。     

Surface properties of ω-perfluorooctyl-alkyl polyacrylates: odd–even effect

A series of ω-perfluorooctyl-alkyl polyacrylates has been prepared and analysed. The odd–even effect, already observed in the case of liquid crystalline polymers has been exhibited for perfluorinated ones. Values of the contact angles to advanced (θ_a), with withdrawal (θ_r), as well as the contact angle hysteresis (Δθ) of various ω-perfluorooctyl-alkyl polyacrylates in water at 20 °C are described. Contrary to the advancing contact angle which is almost independent of spacer length, the receding one varies strongly with it.     

The effect of interface deformation due to gravity on line tension measurement by the capillary rise in a conical tube

Much research has been done on line tension measurement and interpretation, and attempts have also been made to measure line tension with simple, cheap and reliable methods that do not require excessive sophistication. Of particular interest is the method of determining line tensions of solid–liquid–vapor systems from the capillary rise in a conical tube. This simple and relatively inexpensive method gives line tension values comparable to those reported in the literature obtained via highly sophisticated instruments or techniques such as the well known axisymmetric drop shape analysis technique. The absolute value of line tension obtained using the conical tube method and assuming a spherical liquid–vapor interface is larger but of the same order of magnitude (1 μJ m⁻¹) as that reported in the literature. A theoretical analysis presented herein shows that by including the deformation of the liquid–vapor interface due to gravity in the conical capillary analysis, the line tension value inferred from the experimental data is reduced by approximately 50% and compares better with values in the literature obtained using other sophisticated methods. Thus a relatively simple, cheap, accurate and reliable method of line tension measurement has been advanced.     

Density Functional Theory Study on the Adsorption of Dioxygen on Small Pt-Pd Clusters

1 INTRODUCTION The bimetallic nanoclusters are of standing inte- rest since they can exhibit catalytic, electronic and optical properties distinct from those of corre- sponding pure nanoclusters[1～4]. Palladium and pla- tinum, well known for their catalytic properties, are often used as the catalyst in different fuel cells[5～8]. Several experimental results illustrate that for the oxygen reduction reaction (ORR), which is one of the primary reactions taking place in many fuel cells and…     

共线散射体系A+BC的平-振能量传递──无限维李代数处理方法

利用无限维李代数方法处理了在BC分子能谱中含有二级与三级非简谐项的散射体系A＋BC的平-振能量传递问题，获得了散射过程的含有主要动力学参量的跃迁矩阵元和跃迁几率的解析表达式     

原子氧在Ru低指数面及(110),(111)台阶面上的吸附

利用原子与表面簇合物相互作用的5参数Morse势方法(简称5-MP)系统地研究了O-Ru低指数面及Ru(1120),(1121)台阶面体系,获得了吸附几何、结合能、振动频率等临界点特性,所得相关数据与实验结果非常吻合.并且通过理论计算及原子吸附态振动指纹的遗传、遗变特性预言了氧原子在Ru(1121)台阶面的吸附.本文认为氧原子在HCP晶格的金属表面上的吸附倾向于三重位.