单面加热矩形通道热入口段层流对流换热特性的场协同分析

对单面加热矩形通道热入口段的层流对流换热问题进行了数值模拟研究,给出了不同截面比的局部努赛尔数。推导出单面加热时的场协同方程,以此分析了不同截面比下加热边界条件对努赛尔数的影响规律。     

文克尔地基上阶梯式单向矩形薄板的振动

用奇异函数建立文克尔地基上阶梯式单向矩形薄板自由振动和强迫振动的微分方程并求得其通解，用Ｗ算子给出主振型函数的表达式及常见支承条件下板的频率方程，用广义函数讨论板在不同形式载荷作用下的强迫振动响应·     

一种简易的单纯形表

通过对单纯形法的分析和研究,提出了一种简易的单纯形表,并利用矩形法则进行计算而得到一种改进的单纯形法.结果表明该法简单易行,并减少了计算量和存储量.     

逆半群的基本矩形带的同余完备性

本文讨论了逆半群的基本矩形带上的完备同余，就若干特殊情形给出了这类半群是完备的充分必要条件。     

Finite Integral Transform Solutions for Free Vibrations of Rectangular Thin Plates With Mixed Boundary Constraints北大核心CSCD

Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

类比学习路径 重视探究过程——以“矩形的判定”再设计为例

基于对《课标(2022版)》的研读,本文中对“5.1.2矩形的判定”进行再设计.类比平行四边形研究路径,通过对矩形判定定理“引入—发现—猜想—验证—表述—应用”的探究,体现定理学习的一般过程,提高学生思维品质.     

基于驻波能量特征的矩形谐振腔电磁传播模式分析

驻波是大学物理课程内容中的一个重要概念,在实践中有非常广泛的应用.利用驻波的能量特征和分析方法可以对实际应用中很多复杂问题进行高效便捷的分析处理.基于驻波能量特征和分析方法对微波矩形谐振腔中电磁波的传播和能量分布特征进行分析.一方面克服传统分析方法的抽象性和复杂性,另一方面也可以为加强教师和学生对相关概念及其应用的理解提供重要参考.     

矩形微通道中气–非牛顿流体两相流实验研究

本文通过实验研究了空气与非牛顿流体在小尺寸矩形微通道中的两相流动特性,给出了在不同气液两相流速下的流型图。同时比较了气液两相流速,液相黏度,表面张力,微通道尺寸对各流型分布区域以及Taylor气泡/液柱长度的影响。发现气液两相流流速变化对流型区域的影响极为明显,而黏性力和表面张力只是在局部范围改变了流型分布。Taylor气泡长度随气液两相流速比增大而增大,随液相黏度及表面张力增大而减小。液柱长度随液相黏度增大而增大,随两相流速比及表面张力增大而减小。最后,我们给出了基于无量纲数JG/JL,Re和Ca的Taylor气泡/液柱长度预测公式,公式预测结果与实验结果基本一致。     

用矩形栅自动相移法测量三维物体形状

本文介绍了一种自动测量物体三维形状的新方法。该方法将矩形栅投影于三维物体表面，利用图像处理系统自动产生云纹和自动实现云纹相移，实现了三维物体形成恢复。本文通过实验验证了该方法的正确性下处理精度。方法容易实现，能较好消除多种系统误差，抗干扰能力强，精度和自动化程度高。     

箔式高阻值低压锰铜压阻应力计的设计及动态标定

设计了低压锰铜压阻传感器 ,并通过平板撞击实验标定了该传感器在 0 .3～ 9.4GPa范围内的压阻关系。标定曲线在 0 .3～ 1.5GPa范围内是线性的 ,对应的是传感器的弹性状态 ,而在 1.5～ 9.4GPa范围内是二次曲线。标定曲线的拐点在 1.5GPa附近 ,这与理论分析和他人的实验结果相接近。