Rolling of a Rigid Cylinder over a Half-Plane with Initial Stresses (Harmonic and Bartenev–Khazanovich Potentials)

An asymmetric quasistationary problem for a prestressed half-plane with harmonic and Bartenev–Khazanovich potentials is solved based of the linearized theory of elasticity. The Mehler–Fock integral transform is used to solve the differential equations that describe the stress–strain state of the half-plane. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

A Simplified Optimal Control Method for Homoclinic Bifurcations

A simplified optimal control method is presented for controlling or suppressing homoclinic bifurcations of general nonlinear oscillators with one degree-of-freedom. The simplification is based on the addition of an adjustable parameter and a superharmonic excitation in the force term. By solving an optimization problem for the optimal amplitude coefficients of the harmonic and superharmonic excitations to be used as the controlled parameters, the force term as the controller can be designed. By doing so, the control gain and small optimal amplitude coefficients can be obtained at lowest cost. As the adjustable parameter decreases, a gain of some amplitude coefficient ratio is increased to the highest degree, which means that the region where homoclinic intersection does not occur will be enlarged as much as possible, leading to the best possible control performance. Finally, it is shown that the theoretical analysis is in agreement with the numerical simulations on several concerned issues including the identification of the stable and unstable manifolds and the basins of attraction.     

调和函数边界积分方程的充要条件

本文以调和函数的边值问题为例,探讨了边界积分方程的充要条件.文中首次提出了超定问题的概念,并建立了超定问题有解的一个充要条件,它也就是直接变量边界积分方程的一个充要条件.文中首次阐明了边界积分方程与变分原理的内在的联系,还指出了间接变量与直接变量两类边界积分方程之间存在着一一对应的关系.文中的慨念、思路和论点不难用于其它有变分原理的问题的边界积分方程.     

横观各向同性三维热弹性力学通解及其势理论法

通过引入两个位移函数，对用位移表达的运动平衡方程作了简化．利用算子理论，严格地导出了横观各向同性非耦合热弹性动力学问题的通解．对于静力学问题，通解的形式可进一步简化成用4个准调和函数来表示．具体考察了横观各向同性体内平面裂纹上下表面有对称分布温度作用的问题，推广了势理论方法，导出了一个积分方程和一个微分-积分方程．针对币状裂纹表面受均布温度作用情形，给出了具体的解。     

Contact Stress Distribution Under a Rigid Cylinder Rolling Over a Prestressed Strip

A nonsymmetric quasistationary problem for a strip with initial stresses is solved under the linearized theory of elasticity for harmonic and Bartenev–Khazanovich potentials. The Hankel integral transform is used to solve the differential equations that describe the stress–strain state of the strip. The dependences of the normal and tangential stresses and stress intensity factors on the elongation are plotted     

Non-integrability of anisotropic quasi-homogeneous Hamiltonian systems

We consider the anisotropic Hamiltonian systems which potential is made of a finite sum of homogeneous parts of arbitrary degree. For this problem, we prove for two and three degrees of freedom, that there are no more meromorphic integrals than the Hamiltonian itself, except for the classical integrable cases.     

改进的 Morse 势和冲击压缩

用分子动力学方法模拟凝聚介质中一维分子链上的激波传播，以得到与冲击压缩实验相一致的结果。通过比较分子链上的孤立波解与激波的实验结果，提出对分子间Ｍｏｒｓｅ作用势进行与考虑量子效应相一致的修正，从而使分子动力学模拟得到的激波Ｕｓ－Ｕｐ关系与实验结果在波后粒子速度达到声速的范围内一致。     

销钉对FCP电位测试精度影响之BEM分析

本文用边界元法对销钉接触角及销钉孔半径对三种电流输入方式下紧凑拉伸试样的电位函数影响进行了分析。结果证明,人们在电位法测试中常用的电流输入方式容易引起误差,并非最佳方案.最佳方案是另一种同样方便的电流输入方式.     

Regioselective Oxidative Ring Opening of Cyclopropyl Silyl Ethers: A Quantum Chemical Study

In contrast to the structurally and configurationally stable alkyl‐ or aryl‐substituted cyclopropyl radical cations, cyclopropyl silyl ethers undergo spontaneous ring opening upon oxidation whereby the endocyclic C? C(O‐TMS) bond is cleaved with remarkable selectivity. DFT calculations on 1‐trimethylsilyloxybicyclo[4.1.0]heptane show that this selectivity arises from the topology of the potential surface of the corresponding radical cation which is initially generated in a very steep region of the potential surface from where the steepest descent leads to cleavage of the endocyclic rather than the lateral C? C(OTMS) bond. Cleavage of the lateral bond leads to interesting conformational changes which are explored in detail.     

Ionic liquid salt bridge based on tributyl(2-methoxyethyl)phosphonium bis(pentafluoroethanesulfonyl)amide for stable liquid junction potentials in highly diluted aqueous electrolyte solutions

A moderately hydrophobic ionic liquid, tributyl(2-methoxyethyl)phosphonium bis(pentafluoroethanesulfonyl)amide ([TBMOEP⁺][C₂C₂N⁻]), shows a very stable liquid junction potential upon contact with an aqueous solution whose ionic strength is as low as 1 μmol dm⁻³. The stability with the maximum excursion of the potential within ±0.5 mV for 30 min is very promising for accurate determination of pH and other single ion activities potentiometrically.