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.     

粘弹性波动方程的H1-Galerkin时空混合有限元分裂格式

构造一维粘弹性波动方程的H¹-Galerkin时空有限元分裂格式.这种新的分裂格式在时空两个方向同时利用有限元离散,具有H¹-Galerkin混合有限元方法和时空有限元方法的优点,如在不受LBB相容性条件限制的同时能够高精度逼近流体的压力和达西速度,有限元空间可以利用不同次数的多项式空间,能同时得到时间和空间两个变量的形式高阶精度等.通过构造时空投影算子并讨论其相关逼近性质,证明了解的存在唯一性和稳定性,给出混合时空有限元解的误差估计,给出数值算例验证了理论推导结果的合理性和算法的有效性,并和传统H¹-Galerkin方法做比较,得到了更小的误差和超收敛阶.     

新型列车侧墙内装板声学分析、优化及应用*

为了开发与应用新型列车车体降噪内装结构,基于混合FE-SEA法对轨道车辆用新型橡胶泡棉夹芯板进行隔声与声辐射预测建模,并进行了试验验证,进而利用该模型分析了橡胶泡棉孔隙率与芯皮厚度比对其隔声性能、声辐射性能的影响规律,并通过敷设阻尼层优化了其声学性能。最后,在侧墙组合结构的声学设计中评价了其实际应用效果。结果表明：随着孔隙率的逐步下降,橡胶泡棉夹芯板隔声量上升趋势较为明显,而辐射声功率持续降低;随着芯皮厚度比的逐步提高,夹芯板隔声量呈略微上升趋势,辐射声功率则相应降低。在远离声源一侧的橡胶泡棉蒙皮外侧敷设阻尼层的效果最优,优化后夹芯板计权隔声量提高0.7dB,总声功率级降低0.7dB;相较于传统木质胶合板和铝蜂窝板,橡胶泡棉夹芯板相较于传统内装板材在结构隔声设计中具有轻量化优势。     

差动式双波混合干涉微小振动检测系统

针对工业环境下粗糙金属表面微小振动的在线测量需求,提出了一种基于差动式双波混合干涉的微小振动检测系统。该系统将极性相反的高电压分别施加在两块硅酸铋晶体上以得到差动式双路振动解调信号,进而通过差分处理抑制对电压极性不敏感的噪声并提高灵敏度。为验证所提出方案的可行性,分别进行了仿真分析与实验验证。对一粘连在压电陶瓷上的紫铜片进行振动测量实验,并将振动测量结果分别与施加在压电陶瓷上的电压和激光测振仪的测量结果进行对比。结果表明,利用所提出检测系统可准确获得振动信号的频率、相位和幅值信息,与单路式结构相比,差动式双波混合干涉仪的灵敏度提高了一倍,信噪比从27.47 dB提高到了30.83 dB,相对误差的均方根值从3.07%降低到了1.42%。     

多重短程有序准化学模型: 有序原子对的对立与统一

在准化学模型框架下, 假设有序原子对同时具有可区分与不可区分的双重属性, 首先构造了双重短程有序准化学模型, 然后讨论了该模型所能满足的各类理论极限. 经总结提炼, 提出了有序原子对的对立统一理论. 基于该理论, 进一步将双重短程有序准化学模型做了一般化推广, 开发了多重短程有序准化学模型. 该模型能够有效描述二元熔体中存在多重短程有序构型时的热力学行为. 选取了至少存在两重短程有序构型的Bi-K熔体来检验模型的合理性和可靠性. 结果表明, 除配位数外, 只需4个模型参数就能合理再现该二元熔体所有的热化学数据.     

溶液法制备柔性压阻式传感器的研究进展

柔性压阻式传感器具有结构简单、易于制备、检测范围广等优势, 在可穿戴电子器件领域中扮演着非常重要的角色. 在制备柔性压阻式传感器的众多方法中, 溶液法由于操作简单、反应条件温和、材料的适用性广泛、易于规模化制备等优势, 成为极具发展前景的制备工艺. 在此基础上, 如何进一步提高柔性压阻式传感器的力学与电学性能也成为研究者们更加关注的话题. 另外, 制备图案化、微型化、规模化的传感器阵列为柔性压阻式传感器的应用范围拓展了新的道路. 本综述首先介绍了柔性压阻式传感器的工作原理与性能指标, 同时讨论了其性能指标对传感器在实际应用中的影响. 随后, 简单介绍了其构成材料, 并通过梳理近年来溶液法制备柔性传感器的研究成果, 选取了几种典型的溶液法制备方法进行重点介绍, 指出其具备的优势及目前存在的问题. 最后, 对溶液法制备柔性传感器的发展方向进行总结与展望.     

弹性力学的混合方程和Hamilton正则方程

本文指出,在弹性力学基本方程中,按变量分类的位移方程,应力方程以外的第三种混合方程,以及按运算子分类的微分方程、变分原理以外的第三种Hamilton方程,它们正好是对应的。本文讨论了静力的和动力的情况以及它们可能的应用。     

Effects of fibrous fillers on friction and wear properties of polytetrafluoroethylene composites under dry or wet conditions

The friction and wear behavior and mechanism as well as the mechanical properties of polytetrafluoroethylene （PTFE） composites filled with potassium titanate whiskers （PTW） and short carbon fibers （CF） under dry, wet and alkaline conditions were investigated. Experiments indicated that owing to appropriate cooling and boundary lubricating effects, the filled PTFE composites showed much lower frictional coefficient and better wear resistance under alkaline than dry and wet sliding conditions. The wear resistance of carbon-fiber-filled PTFE was much better than that of potassium titanate-whisker-filled PTFE composites in water. Results also showed that the transfer film on counterpart rings was significantly hindered by water and alkali. Hydrophilic-filler-reinforced PTFE composites yield higher wear rate when sliding under water.     

大挠度弯曲直梁混合变量最小势能原理的应用

应用大挠度弯曲直梁混合变量最小势能原理,求解均载两端固定大挠度柱面弯曲板条的轴向挠度分布和轴向弯矩分布．实例计算表明:该方法简单实用、精度高,是一种计算大挠度柱面弯曲板条变形的有效方法．     

A variational solution of 2-D sound-structure interaction problems

Based on the fluid-structure coupling theory, a localized variational principle for analyzing the sound radiation from elastic structure submerged in water due to harmonic excitations is presented. It will be a powerful tool to formulate various numerical methods for steady response of structural-acoustic systems. By means of this variational principle a hybrid element method, in which an analytical solution valid in most of the surrounding water is incorporated with finite elements distributed in the structure and its neighboring water, is devised. Computational examples are then given to demonstrate its high accuracy and time saving. The project supported by the National Natural Science Foundation of China (10172038) and the Doctoral Program Foundation of Institution of Higher Education of China (20040487013). The English text was polished by Yunming Chen.