变厚度环板在面内变温下的固有频率

本文采用薄板线性振动理论分析了厚度沿径向变化和受面内约束的各向同性环形薄板在均匀变温下的自由振动和热弹性稳定性问题。分别针对厚度按指数函数和线性函数变化的两种情况，用有限差分法计算了变厚度环板在内、外周边横向夹紧和简支条件下的线性固有频率和临界温度。由数值结果表明，固有频率的平方与面内变温成线性关系。厚度变化参数、内外半径的比值均对环板的固有频率和临界温度有显著影响。文中给出了丰富的数值结果，可供工程设计参考。     

环形粉末预制坯压制规律研究

研究了环形粉末预制坯压制过程中压力和密度变化规律.通过力学分析建立了环形粉末预制坯压制力学模型,导出了6种压制方式下压制力沿预制坯高度分布规律,建立了统一的压制力分布计算公式,并计算了环形粉末预制坯下端面的最小压制力.基于黄培云粉末压制理论,导出了环形粉末预制坯相对密度沿高度分布计算公式,以及环形粉末预制坯上下端面密度的比值.     

外延生长亚单层Si薄膜的动力学蒙特卡罗模拟

建立了沿Si(100)方向外延生长亚单层Si薄膜的动力学蒙特卡罗模拟模型,对二维Si薄膜的生长过程及二维Si岛的形貌演变进行了研究.结果表明,在一定的入射率下存在一最佳成岛温度,该温度随入射率的增大而升高.以最佳成岛温度生长时,岛密度随覆盖度的增加呈现增加-饱和-减小的变化规律.在低温和高入射率下,岛密度随覆盖度单调增加,薄膜呈离散生长.而温度很高和入射率很低时,岛密度始终以很小的数值在小范围内振荡,薄膜呈紧致生长.     

两环形平面平行度检定及数据处理方法研究

环形平面是指该平面不是长方形或者正方形,而是圆形,部分由于使用需要中间带孔,本文就中间带孔的两环形平面,其中一个在上,一个在下,研究用电子水平仪检定其平行度,并按照平行度定义处理数据,从而得到环形平面的平行度。一、平行度测量如果把两环形平面都放直,则它们都比较狭窄,故可以把对平面的测量,简化为在沿长度方向的截面     

截面任意形状的柱形和环形容器内液体晃动特性的精确解法

本文研究截面任意形状的柱形和环形容器内液体的晃动特性，利用Ｆｏｕｒｉｅｒ级数匹配法将液体速度势沿容器壁面展开得频率方程，由行列式搜根法数值计算各阶固有振动频率，结果是精确的，方法具有通用性。     

基于微分求积法的变密度印刷纸带振动特性分析

采用微分求积法分析纸带面密度沿宽度方向线性变化时运动矩形纸带横向振动问题。建立了印刷运动纸带的横向振动模型。研究了变密度运动矩形纸带的无量纲振动频率与无量纲轴向运动速度、密度系数、纸带张力比之间的关系。数值计算结果表明,用微分求积法求解变密度运动矩形纸带横向振动问题是切实可行的。该研究结果为改善印刷纸带在印刷过程中的动态特性提供了理论依据。     

基于环形线圈的磁场抗扰度试验系统分析

导出了环形线圈的磁感应强度空间分布解析表达式,并通过数值仿真分析了磁感应强度在试验平面上的变化特性和磁场空间分布特性;介绍了用于直流高磁场强度的环形线圈和150kHz～1MHz磁场抗扰度试验系统;最后对分析结果进行了实验验证。     

有机功能薄膜的超高密度信息存储

超高密度信息存储研究是纳米电子学的重要研究领域,有机功能薄膜以其独特的性质有可能成为超高密度信息存储介质之一。利用ＳＴＭ研究了Ｎ,Ｎ－二甲基－Ｎ－（３－硝基苯叉）－对苯二胺（ＤＭＮＢＰＤＡ）有机薄膜的存储特性。高分辨扫描电子显微镜的结果表明,在扫描过程中ＳＴＭ对ＤＭＮＢＰＤＡ薄膜表面进行了二次加工,显微Ｒａｍａｎ谱表明在加工区依然存在着ＤＭＮＢＰＤＡ薄膜,并用原子力显微镜表征了加工区薄膜的表面形貌     

氮化铁梯度薄膜的制备和磁性研究

用对向靶溅射方法制备出氮化铁梯度薄膜。利用X射线光电子能谱（XPS）对样品进行了深度剖面分析：铁原子和氮原子的百分含量沿膜厚方向呈梯度变化。X射线衍射表明膜中含有α－Fe，α”－Fe16N2，ε－FexN（2＜x≤3）和ξ-FeN各相。随着氮分压增加，膜中含氮量高的相比例亦增加，饱和磁通密度逐渐降低。     

氮化铁梯度薄膜的制备和磁性研究

用对向靶溅射方法制行出氮化铁梯度薄膜。利用Ｘ射线光电子能谱（ＸＰＳ）对样品进行了深度剖面分析，铁原子和氮原子的百分含量沿膜厚方向呈梯度变化。Ｘ射线衍射表明膜中含有α＝Ｆｅ，－Ｆｅ１６Ｎ２，ε－ＦｅｘＮ（２〈ｘ≤３）和δ－Ｆｅ２Ｎ各相。随着氮分压增加，膜中含氮量高的相比例亦增加，饱和磁通密度逐渐降低。     

变密度环形薄膜的轴对称振动修正摄动解

采用修正摄动法研究了变密度环形薄膜的轴对称横向固有振动，并求得了确定其横向振动固有频率的特征方程，把该方法所得到的修正摄动解与有关文献所得结果进行比较，可知此修正摄动解不但计算简便，而且精度可与经典的打靶法与微分求积法的精度相当。     

Linearly elastic annular and circular membranes under radial, transverse, and torsional loading. Part II: Vibrations about deformed equilibria

Equilibrium configurations of annular and circular membranes involving large displacements were determined in Part I of this study. Now small vibrations about such equilibrium states are analyzed for annular membranes. The membrane is linearly elastic, initially flat, and taut. Föppl-von Kármán theory is used to obtain the linearized vibration equations. The problems considered include inward and outward radial stretching, transverse displacement at the inner edge, transverse pressure, a vertical distributed load with a vertically sliding outer membrane edge, torsion at the inner edge along with outward stretching, and in-plane vibrations for cases having a flat equilibrium shape. In many of the cases the transverse motion is coupled with radial and circumferential motions. A shooting method is used to obtain vibration frequencies and corresponding vibration modes with different numbers of nodal diameters and nodal circles. The effects of Poisson’s ratio, in-plane radial and circumferential inertias, the ratio of the radii of the inner and outer edges, and the loading magnitude on the vibration frequencies are investigated.     

Linearly elastic annular and circular membranes under radial, transverse, and torsional loading. Part I: large unwrinkled axisymmetric deformations

Three theories for determination of the equilibrium states of initially flat, linearly elastic, rotationally symmetric, taut membranes are considered: Föppl-von Kármán theory, Reissner’s theory, and a new generalization of Reissner’s theory that does not restrict the strains to be small. Attention is focused on annular membranes, but circular membranes are also treated. Large deformations are allowed, and the equilibrium equations are written in terms of transverse, radial, and circumferential displacements. Problems considered include radial stretching, transverse displacement of the inner edge, an adhesive punch pull-off test on a circular blister, transverse pressure, ponding of annular and circular membranes, a vertical distributed load with a vertically sliding outer membrane edge, pull-in (snap-down, jump-to-contact) instability of a MEMS device, torsion of the inner or outer edge of a stretched membrane, and a combination of radial stretching, vertical displacement, and torsion. Results for the three theories are compared. Closed-form solutions are available in a few cases, but usually a shooting method is utilized to obtain numerical solutions for displacements, strains, and stresses. Conditions for the onset of wrinkling are determined. In the second part of this two-part study, small vibrations about equilibrium configurations are analyzed.     

Free asymmetric transverse vibration of polar orthotropic annular sector plate with thickness varying parabolically in radial direction

In the present paper, free asymmetric transverse vibrations of a non-uniform polar orthotropic annular sector plate, with parabolically varying thickness in the radial direction, have been studied on the basis of classical plate theory. The circular edges of the plate are elastically restrained against translation and rotation while the straight (radial) edges are simply-supported. Fourth-order linear differential equations with variable coefficients governing the motion have been solved by using the collocation interpolation technique with Chebyshev points as the interpolating nodes. Frequency parameters of the plate with flexible boundary conditions at the circular edges for some typical values of the taper parameters, the rigidity ratios and the radii ratio have been presented.     

Vibration analysis of radially FGM sectorial plates of variable thickness on elastic foundations

This paper deals with free vibration analysis of radially functionally graded circular and annular sectorial thin plates of variable thickness, resting on the Pasternak elastic foundation. Differential quadrature method (DQM) is used to yield natural frequencies of the circular/annular sectorial plates under simply-supported and clamped boundary conditions on the basis of the classical plate theory (CPT). The inhomogeneity of the plate is characterized by taking exponential variation of Young’s modulus and mass density of the material along the radial direction whereas Poisson’s ratio is assumed to remain constant. The validity of the present solution is first examined by studying the convergence of the frequency parameters. Then, a comparison of results with those available in literature confirms the excellent accuracy of the present approach. Afterwards, the frequency parameters of the circular/annular sectorial thin plates with uniform, linear, and quadratic variations in thickness are computed for different boundary conditions and various values of the material inhomogeneity constants, sector angles, and inner to outer radius ratios.     

Winkler地基上变厚度圆（环）板的非对称自由振动

本文提出了Winkler地基上变厚度圆(环)板非对称自由振动的传递矩阵法.应用贝塞尔函数理论,求得等厚度圆板和环板单元非对称自由振动传递矩阵的正确公式.然后将Winkler地基上的变厚度圆(环)板划分成一系列的等厚度的圆板和环板单元,应用传递矩阵原理得到变厚度圆(环)板的整体传递矩阵公式.最后给出了一些数值结果,表明板厚和地基模量变化对固有频率的影响.     

Vibration of circular and annular plates using finite elements

The finite element method is applied to the free transverse vibration of circular and annular plates of varying thickness. An annular element is derived which incorporates the number of diametral modes in the deflection function. This results in an element having only four degrees of freedom, these being the deflection and slopes at the inner and outer radii of the element at an anti-node of the particular vibration mode. Thickness variation in the radial direction is readily introduced, and stiffness and inertia matrices are presented for elements with linear and parabolic variations in thickness. The method is checked with several numerical examples. Calculations of free vibration of circular and annular plates of constant, linear and parabolic thickness variation are compared with available exact solutions.     

3-D free vibration analysis of thick functionally graded annular sector plates on Pasternak elastic foundation via 2-D differential quadrature method

Early studies on annular sector plate vibrations were focused on two-dimensional theories, such as the classical plate theory and the first- and the higher-order shear deformation plate theories. These plate theories neglect transverse normal deformations and generally assume that a plane stress state of deformation prevails in the plate. These assumptions may be appropriate for thin plates. In this paper, free vibration of thick functionally graded annular sector plates with simply supported radial edges on a two-parameter elastic foundation, based on the three-dimensional theory of elasticity, using differential quadrature method for different circular edge conditions including simply supported-clamped, clamped–clamped, and free-clamped is investigated. A semi-analytical approach composed of differential quadrature method and series solution is adopted to solve the equations of motion. The material properties change continuously through the thickness of the plate, which can vary according to a power law, exponentially, or any other formulations in this direction. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The new results can be used as benchmark solutions for future research.     

Differential quadrature analysis of functionally graded circular and annular sector plates on elastic foundation

The main purpose of this study is to investigate buckling and free vibration behaviors of radially functionally graded circular and annular sector thin plates subjected to uniform in-plane compressive loads and resting on the Pasternak elastic foundation. In-plane compressive loads may be applied to either radial, circumferential, or all edges of circular/annular sector plates. Based on the classical plate theory (CPT), critical buckling loads and fundamental frequencies of the circular/annular sector plates under simply-supported and clamped boundary conditions are obtained by using differential quadrature method (DQM). The inhomogeneity of the plate is characterized by taking exponential variation of Young’s modulus and mass density of the material along the radial direction whereas Poisson’s ratio is considered to be constant. Convergence study is carried out to demonstrate the stability of the present method. To confirm the excellent accuracy of the present approach, a few comparisons are made for limited cases between the present results and those available in literature. Critical buckling load and fundamental frequency parameters of the circular/annular sector thin plates are computed for different boundary conditions, various values of the material inhomogeneity constants, sector angles, and inner to outer radius ratios.     

Mode shapes and frequencies of radially symmetric vibrations of annular sandwich plates of variable thickness

An analysis and numerical results of radially symmetric vibrations of annular sandwich plates with core of linearly varying thickness are presented. The face sheets are treated as membranes of constant thickness, and the core is assumed to be solid as well as moderately thick. Due to linear thickness variation in the core, the face sheets take the shape of a truncated conical shell and because of this the face sheets membrane forces contribute to the bending and transverse shear of the core of the sandwich plate. Keeping this in view, the equations of motion for such a plate are developed by Hamilton’s energy principle. The frequency equations for three different combinations of boundary conditions, namely clamped at the inner edge and clamped or simply supported or free at the outer edge, are obtained by employing the differential quadrature method. The lowest three roots of these frequency equations have been reported as the frequencies for the first three modes of vibration. The effect of various plate parameters such as taper parameter, thickness of the core at the center, face thickness, and radii ratio on the natural frequencies has been analyzed. Three-dimensional mode shapes for a specified plate for all the three boundary conditions are illustrated. A comparison of results is presented.