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.     

Weak Graph Map Homotopy and Its Applications∗

The authors introduce a notion of a weak graph map homotopy (they call it M-homotopy), discuss its properties and applications. They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001. The difference between them is that the weak graph map homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over the graph homotopy transformation. As its applications, they investigate the mapping class group of a graph and the 1-order MP-homotopy group of a pointed simple graph. Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.     

CHAOS FOR MIXING TRANSFORMATIONS

ＣＨＡＯＳＦＯＲＭＩＸＩＮＧＴＲＡＮＳＦＯＲＭＡＴＩＯＮＳ￥ＬＩＡＯＧＯＮＧＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈａｎｇｃｈｕｎ１３００２３,Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｆｏｒａｃｌａｓｓｏｆｍ...     

Integrability and ergodicity of classical billiards in a magnetic field

We consider classical billiards in plane, connected, but not necessarily bounded domains. The charged billiard ball is immersed in a homogeneous, stationary magnetic field perpendicular to the plane. The part of dynamics which is not trivially integrable can be described by a bouncing map. We compute a general expression for the Jacobian matrix of this map, which allows us to determine stability and bifurcation values of specific periodic orbits. In some cases, the bouncing map is a twist map and admits a generating function. We give a general form for this function which is useful to do perturbative calculations and to classify periodic orbits. We prove that billiards in convex domains with sufficiently smooth boundaries possess invariant tori corresponding to skipping trajectories. Moreover, in strong field we construct adiabatic invariants over exponentially large times. To some extent, these results remain true for a class of nonconvex billiards. On the other hand, we present evidence that the billiard in a square is ergodic for some large enough values of the magnetic field. A numerical study reveals that the scattering on two circles is essentially chaotic.     

Almost linearity of -bi-Lipschitz maps between real Banach spaces

Let and be real Banach spaces. A map between and is called an -bi-Lipschitz map if for all . In this note we show that if is an -bi-Lipschitz map with from onto , then is almost linear. We also show that if is a surjective -bi-Lipschitz map with , then there exists a linear isomorphism such that

where as and .

     

Crumpled laminations and manifolds of nonfinite type

Using a group-theoretic construction due to Bestvina and Brady, we build -manifolds which admit partitions into closed, connected -manifolds but which do not have finite homotopy type.

     

Reaction potential map analysis of chemical reactivity—III

Reaction potential maps (RPM) have been introduced as a new tool for the study of molecular reactivity. The equipotential energy maps, which are created on given planes around a molecule, define reaction contours towards specific counter-reagent models and are evaluated by perturbation theory. Since the calculated interaction energy involves electrostatic, polarization, exchange, and charge transfer energies, the RPM's can be used to predict site selectivity in a variety of chemical reactions. We found that the calculated RPM's of the SCN^– anion explained well the experimental observations that it reacts at the S atom with soft electrophiles and at the N atom with hard electrophiles. The difference in reactivity between SCN^– and OCN^– was clearly shown by the RPM's of these anions. The ambident nucleophilic nature of the NO ₂ ^– and the CH₂CHO^– anions was also well represented by their RPM's.     

高中有机化学教材“烃类化合物”的国际比较研究

基于闫春更等建立的二维度四指标教材难度微观评价模型，重点对中国、美国、新加坡、澳大利亚、日本、英国的高中化学教材中"烃类化合物"内容的整合广度、表征深度进行测评和比较。研究发现6国教材内容的整合广度整体上差异不大，但其表征深度差异明显；美国教材注重学生认识物质的思路和方法的渗透，日本教材注重基本知识与技能的掌握，中国教材将概念诠释与样例分析相融合；英国、新加坡、美国教材注重情境推理或比较等信息处理策略的运用，对学习者学习的引导性较强。     

可调移动重叠分离图法用于高效液相色谱多台阶梯度分离条件优化的研究

计算机辅助高效液相色谱（HPLC）分离条件优化可以低成本、快速地得到优化的分离条,因而已较为广泛地用于复杂样品的分离分析。基于移动重叠分离图方法,又发展了一种新型的多台阶梯度分离条件的优化方法可调移动重叠分离图法。该方法通过预测不同流动相条件下各组分的保留时间、峰宽和分离度,绘制出对于样品中各组分的重叠分离区域图。在对当前台阶流动相组成进行优化的同时,考虑其对后面一到两个台阶上流出组分保留的影响,实时地重新绘制对于后面台阶上流出组分的重叠分离区域图。通过观察当前台阶流动相条件对当前台阶和后面台阶上流出组分分离的影响,综合考虑样品中所有组分的分离情况,找到更接近全局最优的分离条件。通过扫描的方法对优化得到的分离条件进行微调,能够进一步提高分离效果。采用文献数据对可调移动重叠分离图法的应用加以说明,在二元流动相体系下,证明了该方法在HPLC方法建立方面的优越性。     

共聚高分子混合物的分子热力学模型

以硬球链流体的分子热力学模型为基础 ,引入方阱位能相互作用的贡献 ,建立了共聚高分子混合物的分子热力学模型 .模型中具有物理意义的链节参数 (链节数、链节直径和链节间的相互作用能 )由纯物质的pVT关系拟合得到 ,而用来校正交叉作用能和交叉碰撞直径的可调参数需由液液平衡的实验数据回归得到 .采用了相对简单的处理方法来确定这些可调参数 .对所选共聚高分子混合物的共存曲线、互溶窗和互溶图等相行为的关联结果令人满意 .