有厚度平板尾缘可压缩剪切层中的涡结构数值模拟

采用一个新型Fu Ma高精度UCD5 SCD6紧致差分算法,通过直接求解二维Navier Stokes方程,成功实现了有厚度平板尾缘可压缩剪切层中涡结构的数值模拟,并考查了平板厚度对其的影响.计算对流马赫数M_c=0.3,平板厚度分别为1,2,3,4个参考长度.结果表明,增加平板厚度可促使平板尾缘可压缩剪切层中的涡提前卷起,有利于两股气流混合.     

变厚度圆板、环板振动分析的传递矩阵法*

变厚度圆板和环板是在工程设计中经常遇到的一类构件,与等厚度板相比,通过适当的沿径向厚度的变化,这种变厚度板在振动、失稳、弯曲等方面能起到更好的效果。将沿径向任意变厚度圆板、环板划分为一系列等厚度环板单元,基于Mindlin中厚板理论采用逆向推导的方式推导了其传递矩阵,建立起变厚度圆板、环板的频率方程。通过计算线性变厚度环板自由振动时的频率,并与ANSYS模态分析结果相比较,验证了计算模型的精确性。逆向推导法避免了高阶数传递矩阵推导复杂的问题,是对传递矩阵法的很好推广。     

使用移测显微镜测量平行平板的折射率

依据折射定律,通过移测显微镜测量光线经平行平板产生的位移,确定平行平板的折射率.利用不确定度分析,给出入射角和平板厚度测量范围的建议,并分析了显微镜系统景深对平行平板厚度的限制.实际测量结果与利用阿贝折射仪的测量结果一致,该实验可作为基础物理实验中折射率测量相关实验项目的拓展.     

临界厚度d_0和纵场临界电流曲线

本简报对理想第二类超导平板的纵场临界电流曲线进行的分析表明了,当平板厚度d大于临界厚度d_0时,曲线呈倒U字形;当d小于d_0时,曲线呈现出峰值效应。     

基于平板模型的X射线散射特性研究

 为了进一步研究高能X光散射的特性,以平板为模型,通过解析方法和蒙特卡罗（MC）数值模拟研究了X光散射的规律。研究结果表明：高能X光的散射以康普顿散射为主,当平板厚度相应的X光光程小于2.0时,平板散射中的一次康普顿散射超过75%;当到达探测器的散射照射量最大时,平板厚度相应的X光光程介于1.0与2.0之间。     

玻璃平板厚度测量的实验研究

平板玻璃生产中需要对玻璃厚度进行精确地测量。本文通过理论模拟和实验研究了应用白光干涉测量技术,来测量玻璃平板厚度的方法。系统通过步进电机控制精密平移台的移动,实测了一个标称厚度为5mm的玻璃平板,通过多次采样取平均的方法,结果误差为0.34%。     

热声制冷机回热器的构形优化

用构形理论对热声制冷机平板型回热器进行了优化,导出了最优平板间距及最优平板数的解析式,讨论了运行频率、温度梯度、以及平板厚度对最优平板间距的影响,所得结论对实际热声制冷机的设计工作具有一定的理论指导意义。     

快中子照相中的点扩展函数计算

 快中子照相中,基于反冲核原理探测快中子的有机闪烁体平板是普遍采用的快中子辐射转换体。模拟了D-T中子垂直入射BC400闪烁体平板,计算了不同厚度平板闪烁体的点扩展函数,对14.1 MeV快中子照相中闪烁体固有分辨率随厚度的变化进行了研究。计算结果表明,在不考虑二次中子与闪烁体作用及背景噪声等情况时,点扩展函数几乎不依赖于闪烁体厚度。同时,计算还表明在一定的分辨率范围内,由于荧光收集效率的限制,闪烁体厚度增加并不会改善图像对比度。     

近表面层黏性模量梯度变化的复合平板中激光热弹激发声表面波的传播特性

考虑复合平板近表面层的黏性模量变化特性,建立激光在复合平板中热弹激发声表面波的有限元模型,系统研究复合平板中声表面波的传播特性,并讨论近表面层的黏性模量、厚度与Lamé常数对声表面波衰减特性的影响,在此基础上,结合理论计算的色散与衰减曲线对声表面波传播特性进行验证.本研究为激光超声技术无损评估复合平板近表面层的力学性能提供理论指导,同时也为研究复合平板表面微裂纹问题提供可行性思路.     

临界厚度d0和纵场临界电流曲线

本简报对理想第二类超导平板的纵场临界电流曲线进行的分析表明了,当平板厚度d大于临界厚度d₀时,曲线呈倒U字形;当d小于d₀时,曲线呈现出峰值效应。 关键词：     

Vibration of tapered Mindlin plates in terms of static Timoshenko beam functions

In this paper, the free vibrations of rectangular Mindlin plates with variable thickness in one or two directions are investigated. The thickness variation of the plate is continuous and can be represented by a power function of the rectangular co-ordinates. A wide range of tapered rectangular plates can be described by giving various index values to the power function. Two sets of new admissible functions are developed, respectively, to approximate the flexural displacement and the angle of rotation due to bending of the plate. The eigenfrequency equation is obtained by using the Rayleigh-Ritz method. The complete solutions of displacement and angle of rotation due to bending for a tapered Timoshenko beam (a strip taken from the tapered Mindlin plate in some direction) under a Taylor series of static load have been derived, which are used as the admissible functions of the rectangular Mindlin plates with taper thickness in one or two directions. Unlike conventional admissible functions which are independent of the thickness variation of the plate, the static Timoshenko beam functions presented in this paper are closely connected with the thickness variation of the plate so that higher accuracy and more rapid convergence can be expected. Some numerical results are furnished for both truncated Mindlin plates and sharp-ended Mindlin plates. On the basis of convergence study and comparison with available results in literature, it is shown that the first few eigenfrequencies can be obtained with quite satisfactory accuracy by using only a small number of terms of the static Timoshenko beam functions.     

Vibration and stability of a circular plate of unidirectionally varying thickness

An analysis is presented for the vibration and stability of an elastically restrained circular plate of unidirectionally varying thickness subjected to an in-plane force. For this purpose, the transverse deflection of a circular plate of variable thickness is written in a series of the deflection functions of a uniform circular plate without the action of a force. The dynamical energies of the plate are evaluated analytically, and the frequency equation of the plate is derived by the Ritz method. The analysis is applied to circular plates of unidirectionally tapered or stepped thickness; the natural frequencies and the divergence loads are calculated numerically, and the effects of the varying thickness and edge conditions on the vibration and stability are studied.     

EFFECT OF ELASTIC FOUNDATION ON ASYMMETRIC VIBRATION OF POLAR ORTHOTROPIC LINEARLY TAPERED CIRCULAR PLATES

Asymmetric vibrations of polar orthotropic circular plates of linearly varying thickness resting on an elastic foundation of Winkler type are discussed on the basis of the classical plate theory. Ritz method has been employed to obtain the natural frequencies of vibration using the functions based upon the static deflection of polar orthotropic plates, which has faster rate of convergence as compared to the polynomial co-ordinate functions. Frequency parameter of the plate with elastically restrained edge conditions are presented for various values of taper parameter, rigidity ratio and foundation parameter. A comparison of the results with those available in the literature obtained by finite element method, receptance method and polynomial co-ordinate functions shows an excellent agreement.     

Free vibration analysis of continuous rectangular plates

Vibration characteristics of rectangular plates continuous over full range line supports or partial line supports have been studied by using a discrete method. Concentrated loads with Heaviside unit functions and Dirac delta functions are used to simulate the line supports. The fundamental differential equations are established for the bending problem of the continuous plate. By transforming these differential equations into integral equations and using the trapezoidal rule of the approximate numerical integration, the solution of these equations is obtained. Green function which is the solution of deflection of the bending problem of plate is used to obtain the characteristic equation of the free vibration. The effects of the line support, the variable thickness and aspect ratio on the frequencies and mode shapes are considered. By comparing the numerical results obtained by the present method with those previously published, the efficiency and accuracy of the present method are investigated.     

An approximate solution for the bending vibrations of a combination of rectangular thin plates

The appropriate method often used for calculating the bending vibration of a single rectangular plate is extended to calculate the bending vibrations of a global system of combinations of rectangular plates with elastically supported and damped non-coupled edges. Two examples, a series of T-combinations and an L-combination of rectangular thin isotropic plates, are considered and the input and transfer mobilities due to point excitation derived. Numerical results are presented for the case of combinations of concrete plates and the effects of varying the material damping of the plates and edge damping are investigated.The eigenfrequencies of an L-combination of plates with one plate of very high bending stiffness are calculated and results compare well with the eigenfrequencies of a single plate calculated by means of the classical Ritz-Rayleigh method.     

Vibrations of circular plates of variable thickness under an inplane force

The natural frequencies of a circular plate of variable thickness under the action of an inplane force are discussed on the basis of the classical theory of plates. The governing differential equation of motion is solved by the method of Frobenius. Frequency parameters of clamped as well as simply supported plates in the first two modes of vibration are computed for various values of a taper parameter, β, and the inplane force, both for linear and parabolic variations of thickness.     

Transverse vibrations of circular plates of varying thickness with non-uniform edge constraints

Free vibrations of circular plates varying in thickness and with flexible edge supports have been studied by several investigators for the restricted case when the supports are represented by uniformly distributed springs of constant stiffness.In the present study an approximate method is presented for dealing with supports possessing rotational flexibility which varies arbitrarily around the boundary.The method consists in representing the varying stiffness in terms of a Fourier expansion in the polar angle and approximately expressing the displacement function using a summation of polynomial co-ordinate functions which exactly satisfies only the essential boundary condition. The Ritz method is then applied in order to obtain the frequency determinant. The method can be easily extended to the forced vibrations case.     

Index to volume 95

The linear and non-linear (large amplitude), axisymmetric free vibration of a circular plate of variable thickness, with immovable edges, is analyzed by applying the transfer matrix method. Two types of circular plate are studied: the stepped thickness plate and the continuously variable thickness plate. Numerical calculations are carried out for these two types of plate, with both simply supported and clamped edges, and the backbone curves and mode shapes are determined. The results are compared with those of other authors.     

Vibration and stability of a variable thickness annular plate subjected to a torque

The free vibration and stability of a variable thickness annular plate subjected to a torque are analyzed by the Ritz method. For this purpose, the transverse deflection of an annular plate is written in a series of the deflection functions of a uniform thickness annular plate without the action of a torque. The kinetic and strain energies of the plate are evaluated analytically and the frequency equation of the plate is derived by the conditions for a stationary value of the Lagrange functional. The present method is applied to annular plates with two types of radial thickness variation, power law and exponential, and the natural frequencies (the frequency parameters) and the divergence torques are calculated numerically, from which the effects of the varying thickness, inner/outer radii ratio and edge conditions are studied.