光滑圆柱体上运动软链的支持力分布

文章导出了光滑圆柱体上软链所受支持力的分布公式,并以此讨论了软链开始脱离圆柱体的条件.     

基于相位相关的柱面全景图像自动拼接算法

提出了一种基于相位相关法的柱面全景图像自动拼接算法.首先推导了柱面投影公式、柱面平移量和平面平移量之间的对应公式;然后利用改进的相位相关法计算出归一化相位相关度的峰值及峰值点坐标,利用峰值作为相关度准则判断两幅图像是否存在重叠部分,利用最大相关度求交自动确定头尾图像,利用峰值点坐标判断两幅相邻网像的位置关系;最后将环绕拍摄的序列图像投影到柱面坐标系下,根据计算得到的变换参数进行图像拼接并融合得到柱面全景图像.实验结果表明,该算法能有效地实现顺序混乱的序列图像的自动排序和柱面全景图像拼接,具有较高的稳健性和拼接精度.     

共轴柱面光学系统的空间光线追迹

本文推导了共轴柱面光学系统的空间光线追迹公式,并讨论和说明公式组在使用中的几个有关问题。     

测定圆柱体杨氏模量的原理分析

分析了测量圆柱体弯曲形变杨氏模量的实验原理,得出了理论公式,将测量拉压形变、弯曲形变的杨氏模量以及扭转形变的剪切模量3个实验中样品形状统一成圆柱体.     

柱面座标系中的磁场拟合

本文介绍柱面座标中的磁场模式。对于内空的磁场,只要测得磁场边界上的B_Z值,即可通过富里哀拟合,精确地计算圆柱体内部的磁场。基于此模式的计算程序得到与实验测量值符合得很好的计算结果。     

激光对运动圆柱体加热的几何学研究

 当激光无论从地面或是从空中辐照运动的圆柱体时，都涉及到入射激光相对于圆柱体的辐照方式。在一定假设下，导出了激光对抛射圆柱体表面加热时圆柱表面热加载功率密度分布公式，并结合一理想情况，针对光束入射角度因子、光斑中心的偏移、光斑形状的变化进行了解析计算分析。分析表明，即使圆柱体本身不做自转，圆柱体表面的光强分布中心也会发生偏移，分布也会发生变化，尤其沿圆柱体轴向的分布变化较大，必须结合实际加以细化研究。     

一种基于光学三角法的形貌测量系统

提出了一种基于光学三角原理的物体形貌测量方法。从理论上推导出了被测点的相对高度与像点距离的线性公式,通过这个公式可以由像点距离计算出被测点的高度。在实际的测量系统中,通过工作台的精确位移和像点的移动距离可标定出线性公式中的未知系数。把被测物体放在工作台上,先测出被测点的像的相对位移,然后再通过公式计算出被测点相对屏幕的距离。试验中测量了一个圆柱体上的一些点的三维坐标,通过这些数据绘出了圆柱体的三维形貌。     

透射式柱面弯晶谱仪的单滤片能量刻度方法

根据布拉格衍射定律和晶层模型,推导了透射式柱面弯晶谱仪的三维衍射光路的理论公式,并利用该理论研究了谱仪测量光谱的能量刻度问题。在考虑了实验中谱仪与光源的准直度和记录介质放置姿态带来的误差后,发现利用多种滤片的K吸收边进行公式拟合得到弯晶谱仪能量刻度曲线的方法对低能X射线谱线的误差较大,进而提出了用单滤片通过理论公式模拟计算进行谱仪能量刻度的方法。通过对透射式柱面弯晶谱仪测量到的Ag靶X光机的实验光谱进行能量刻度,实现了用单滤片在线定标弯晶谱仪,验证了理论公式和能量刻度方法的正确性。     

截面为矩形的无限长载流柱面磁场的空间分布

根据面电流在空间某点的磁场公式和场强叠加原理,求出了截面为矩形的无限长载流柱面空间磁场分布的普遍表达式。     

柱面非线性麦克斯韦方程组的行波解

柱面电磁波在各种非均匀非线性介质中的传播问题具有非常重要的研究价值.对描述该问题的柱面非线性麦克斯韦方程组进行精确求解,则是最近几年新兴的研究热点.但由于非线性偏微分方程组的极端复杂性,针对任意初边值条件的精确求解在客观上具有极高的难度,已有工作仅解决了柱面电磁波在指数非线性因子的非色散介质中的传播情况.因此,针对更为确定的物理场景,寻求能够精确描述其中更为广泛的物理性质的解,是一种更为有效的处理方法.本文讨论了具有任意非线性因子与幂律非均匀因子的非色散介质中柱面麦克斯韦方程组的行波精确解,理论分析表明这种情况下柱面电磁波的电场分量E已不存在通常形如E=g(r-kt)的平面行波解;继而通过适当的变量替换与求解相应的非线性常微分方程,给出电场分量E=g(lnr-kt)形式的广义行波解,并以例子展示所得到的解中蕴含的类似于自陡效应的物理现象.     

Large amplitude vibration of an initially stressed cross ply laminated plates

In this paper, nonlinear equations of large amplitude vibration for a laminated plate in a general state of nonuniform initial stress are derived. The equations include the effects of transverse shear and rotary inertia. Using these derived governing equations, the large amplitude vibration behaviour of an initially stressed cross-ply laminated plate is studied. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the plane of the plate. The Galerkin method is used to reduce the governing nonlinear partial differential equations to ordinary nonlinear differential equations and the Runge-Kutta method is used to obtain the nonlinear to linear frequencies. The frequency responses of nonlinear vibration are sensitive of the vibration amplitude, aspect ratio, thickness ratio, modulus ratio, stack sequence, layer number and state of initial stresses. The effects of various parameters on the large amplitude free vibrations are presented.     

Residual vibration reduction of a flexible beam deploying from a translating hub

This paper presents a method for reducing the residual vibration of a flexible beam deployed from a translating hub. Whereas previous studies have discussed reducing vibration in translating constant-length beams, this study investigates a vibration reduction method for translating beams of variable length. The partial differential equation of motion for a translating beam is derived and transformed into a variational equation. Based on the discretized equations from the variational equation, the dynamic responses of the flexible beam under translation are analyzed. A vibration reduction method is proposed that is effective for both constant- and variable-length deploying translating beams.     

Free vibration of three-dimensional anisotropic layered composite nanoplates based on modified couple-stress theory

Based on the modified couple-stress theory, three-dimensional analytical solutions of free vibration of a simply supported, multilayered and anisotropic composite nanoplate are derived by solving an eigenvalue system and using the propagator matrix method. By expanding the solutions of the extended displacements in terms of two-dimensional Fourier series, the final governing equations of motion with modified couple-stress effect are reduced to an eigenvalue system of ordinary differential equations. Analytical expressions for the natural frequencies and mode shapes of multilayered anisotropic composite plates with modified couple-stress effect are then derived via the propagator matrix method. Numerical examples are carried out for homogeneous thick-plates and sandwich composite plates to show the effect of the non-local parameter in different layers and stacking sequence on the mode shapes. The present solutions can serve as benchmarks to various thick-plate theories and numerical methods, and could be further useful for designing layered composite structures involving small scale.     

Study of the sandwiched piezoelectric ultrasonic torsional transducer

The sandwiched piezoelectric ultrasonic torsional transducer was studied. The transducer consists of front and back metal cylinders, and coaxially segmented, tangentially polarized, piezoelectric ceramic tubes. The torsional vibration of the tangentially polarized piezoelectric ceramic slender tube was studied first and its electromechanical equivalent circuit was derived. Based on the network theory and the electromechanical equivalent circuit, the torsional vibration of the piezoelectric ceramic cylinder, formed by stacking a number of identical short piezoelectric ceramic rings, was analysed and the electromechanical equivalent circuit of the piezoelectric ceramic stack in torsional vibration was developed. Finally, the sandwiched ultrasonic torsional transducer was studied and resonance frequency equations were derived which can be used to design and calculate the torsional transducers for different applications.     

受曲面约束弹性细杆的平衡问题

作为DNA等一类生物大分子的力学模型，弹性细杆的非线性力学再次受到关注，形成一个力学与分子生物学的交叉学科.除了不受外界约束的自由弹性细杆外，受曲面约束的弹性细杆静力学具有重要的应用背景.在分析约束、约束方程和约束力的基础上建立了受曲面约束的圆截面弹性细杆的平衡微分方程，即曲面上的Kirchhoff方程，它是以截面主矢和截面姿态坐标以及中心线的Descartes坐标为变量的微分/代数方程.作为应用，讨论了约束是圆柱面的情形.此时平衡的无量纲方程仅含的物理参数是截面对形心的抗扭刚度和对主轴的抗弯刚度的比值，与几何参数无关.由此导出方程的螺旋杆特解.数值计算表明，对弹性细杆中心线的几何形状有显著影响的是截面主矢和姿态坐标及其导数的起始值，而不是物理参数. 关键词： 弹性细杆 DNA超螺旋 曲面约束 螺旋杆     

Effect of one-way clutch on the nonlinear vibration of belt-drive systems with a continuous belt model

This study focuses on the nonlinear steady-state response of a belt-drive system with a one-way clutch. A dynamic model is established to describe the rotations of the driving pulley, the driven pulley, and the accessory shaft. Moreover, the model considers the transverse vibration of the translating belt spans for the first time in belt-drive systems coupled with a one-way clutch. The excitation of the belt-drive system is derived from periodic fluctuation of the driving pulley. In automotive systems, this kind of fluctuation is induced by the engine firing harmonic pulsations. The derived coupled discrete–continuous nonlinear equations consist of integro-partial-differential equations and piece-wise ordinary differential equations. Using the Galerkin truncation, a set of nonlinear ordinary differential equations is obtained from the integro-partial-differential equations. Applying the Runge–Kutta time discretization, the time histories of the dynamic response are numerically solved for the driven pulley and the accessory shaft and the translating belt spans. The resonance areas of the coupled belt-drive system are determined using the frequency sweep. The effects of the one-way clutch on the belt-drive system are studied by comparing the frequency–response curves of the translating belt with and without one-way clutch device. Furthermore, the results of 2-term and 4-term Galerkin truncation are compared to determine the numerical convergence. Moreover, parametric studies are conducted to understand the effects of the system parameters on the nonlinear steady-state response. It is concluded that one-way clutch not only decreases the resonance amplitude of the driven pulley and shaft's rotational vibration, but also reduces the resonance region of the belt's transverse vibration.     

矩形辐射器压电多频超声换能器的研究

研究了一种具有多个共振频率的矩形辐射器夹心式超声换能器,换能器由圆柱形后盖板、压电陶瓷晶堆及矩形六面体辐射器前盖板组合而成。利用表观弹性法和一维近似理论给出了多频换能器横向及纵向理论共振频率方程。对一种特殊情况下的此类换能器进行了有限元及实验分析,给出了各自的频率输入导纳曲线。对理论和实验结果进行分析后表明,此类矩形辐射器夹心式超声换能器可以在不同的振动模态上工作,具有多个共振频率.     

Entropy production in the flow over a swirling stretchable cylinder

In the present work, the entropy generation due to the heat transfer and fluid friction irreversibility is investigated numerically for a three-dimensional flow induced by rotating and stretching motion of a cylinder. The isothermal boundary conditions are taken into account for the heat transfer analysis. The similarity transformations are utilized to convert the governing partial differential equations to ordinary differential equations. Resulting nonlinear differential equations are solved using a numerical scheme. Expressions for the entropy generation number, the Nusselt number and the Bejan number are obtained and discussed through graphs for various physical parameters. An analysis has been made to compare the heat transfer irreversibility with fluid friction irreversibility using the expression of the Bejan number. It is found that the surface is a durable source of irreversibility and the curvature of cylinder is to enhance the fluid friction irreversibility.     

On radially symmetric vibrations of orthotropic non-uniform disks including shear deformation

This paper deals with the free axisymmetric vibrations of orthotropic circular plates with linear variation in thickness. The analysis is based on a set of two differential equations derived by an extension of Mindlin's shear theory for plates. On simplification and algebraic manipulation, one of the dependent variables is eliminated from the governing equations of motion, giving rise to a fourth order linear differential equation with variable coefficients. The resulting differential equation is solved numerically by the Chebyshev collocation technique. Frequencies and mode shapes for the first five modes of vibration are computed for different plates.     

Exact solutions to a class of nonlinear Schrödinger-type equations

A class of nonlinear Schrödinger-type equations, including the Rangwala-Rao equation, the Gerdjikov-Ivanov equation, the Chen-Lee-Lin equation and the Ablowitz-Ramani-Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary higher order ordinary differential equations (sub-ODEs for short).