Application of Equivalent Air Gap Method in Uniaxial Crystal Plate

The equivalent air gap method is a simple way to trace the ray propagation in an isotropic medium, but it cannot be applied to an anisotropic medium. We present the exact general expressions of the equivalent air gap thicknesses and the displacements for the plane-parallel uniaxial crystal plates. They are also suitable for the isotropie medium. This method is useful when one determines whether certain size plane-parallel plates can be fitted into the available air of an optical system, and also in the prism system design.     

DYNAMIC CHARACTERISTICS IN INCOMPRESSIBLE HYPERELASTIC CYLINDRICAL MEMBRANES

In this paper, the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface. A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained. Some interesting conclusions are proposed for different materials, such as the neo-Hookean material, the Mooney-Rivlin material and the Rivlin-Saunders material. Firstly, the bifurcation conditions depending on the material parameters and the pressure loads are determined. Secondly, the conditions of periodic motion are presented in detail for membranes composed of different materials. Meanwhile, numerical simulations are also provided.     

横观各向同性热弹性梁的精化理论

本文从横观各向同性梁的二维问题出发,研究了横观各向同性热弹性梁的精化理论。首先,在不作任何预先假设的条件下,利用横观各向同性热弹性理论和Lur’e算子函数,获得了由梁中线上的物理量表示的位移场和应力场。对热弹性梁上下表面承受非齐次边界条件的情况,推导出梁的近似控制微分方程。再舍去温度项,则横观各向同性热弹性梁的精化理论退化为横观各向同性梁的精化理论。     

Stress field of orthotropic cylinder subjected to axial compression

Based on the constancy hypothesis of material volume, the circumferential and radial stresses of a cylinder specimen are analyzed when the cylinder is subject to a loading along the axial direction. The circumferential and radial stress distribution is a power function of radius parameter when the constitutive relation of specimen material is orthotropic. The stress distribution is a quadratic function of radius parameter for transversely isotropic material. Along the cylinder axial line, the circumferential and radial stresses are maximum and equal to each other. In the circumference boundary surface, the radial stress is zero and the circumferential stress value is minimal. The failure theory of maximum tensile circumferential strain is applied to calculate the critical axial loading. The circumference-boundary-layer failure criterion of orthotropic cylinders is described with the Hill-Tsai strength theory. The obtained strength theory is related to axial stress and mechanical properties of specimen material and to the specimen axialdeformation strain rate and the change rate of strain rate.     

Piezoelectric transducer parameter selection for exciting a single mode from multiple modes of Lamb waves

Excitation and propagation of Lamb waves by using rectangular and circular piezoelectric transducers surface-bonded to an isotropic plate are investigated in this work. Analytical stain wave solutions are derived for the two transducer shapes, giving the responses of these transducers in Lamb wave fields. The analytical study is supported by a numerical simulation using the finite element method. Symmetric and antisymmetric components in the wave propagation responses are inspected in detail with respect to test parameters such as the transducer geometry, the length and the excitation frequency. By placing only one piezoelectric transducer on the top or the bottom surface of the plate and weakening the strength of one mode while enhancing the strength of the other modes to find the centre frequency, with which the peak wave amplitude ratio between the S0 and A0 modes is maximum, a single mode excitation from the multiple modes of the Lamb waves can be achieved approximately. Experimental data are presented to show the validity of the analyses. The results are used to optimize the Lamb wave detection system.     

二维类正方阿基米德格子声子晶体弹性剪切波能带结构研究

利用平面波展开法研究了二维类正方阿基米德格子(ladybug和bathroom)铝/环氧树脂声子晶体弹性剪切波能带结构.与正方晶格相比,ladybug和bathroom格子都存在高频带隙,而且bathroom格子带隙较宽;ladybug格子有两个各向同性带隙;在相同r0/a(散射体半径与其相邻中心距离比)情况下,分析了ladybug、bathroom格子和正方晶格声子晶体r0/a的变化对带隙相对宽度的影响, 表明类正方阿基米德格子比正方晶格更容易获得带隙.     

横观各向同性饱和弹性半空间地基上圆环板的简谐振动

本文基于在L~2[a,b]上的完备正交函数组,通过将板的挠度、荷载、地基反力及板下地基表面的沉降展开为Fourier-Bessel级数,利用解析法对横观各向同性饱和弹性半空间地基上圆环板的简谐振动进行了系统分析.这些级数中的待定系数由板的边界条件、板的控制方程及板.地基的相容条件加以确定,从而将饱和弹性半空间地基与圆环板的动力相互作用问题转化为代数方程组的求解问题.数值计算表明,该级数解答具有较快的收敛速度.     

各向同性压缩过程中圆盘体系的基本性质

结合理论分析与数值模拟研究仅有线性排斥力的二维无序圆盘体系在准静态各向同性压缩过程中的基本性质.引入平均约化重叠量、约化压强等概念,基于微观的力学分析,导出约化压强与体系的组成成分、几何统计量及形变统计量之间的关系.基于数值模拟结果,讨论平均接触数增量、各种接触类型的百分比、平均约化重叠量、约化压强等物理量在大范围压缩的过程中随体积分数增量的变化,给出一个形式简洁的近似约化压强公式.模拟结果表明圆盘体系在远离临界阻塞态及接近临界阻塞态时的压缩响应不同.     

准各向同性导体指数损耗分析北大核心

高温超导材料具有弱连接和低钉扎力的特性,当超导中通入交流时,导体内磁通线的运动需克服钉扎力,导致焦耳热损耗,即指数损耗,特别是通入的电流接近于临界电流时,该损耗不可忽略。运用数值仿真的方法分析了由第二代高温超导带材构成的准各向同性高温超导股线的指数损耗的特点。研究表明:指数损耗在股线中的分布与磁场的分布密切相关,即处于股线外侧的超导带材的指数损耗要远大于内侧的超导带材;股线总的指数损耗随着通入的电流的增大呈指数倍的增加。