A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

Assembling hydrodynamic cloaks to conceal complex objects from drag

Transformation hydrodynamics and the corresponding metamaterials have been proposed as a means to exclude the drag force acting on an object. Here, we report a strategy to deploy the hydrodynamic cloaks in a more practical manner by assembling different-shaped cloaking parts. Our strategy is to first model a square-shaped cloak and a carpet cloak and then combine them to conceal a more complex-shaped space in the three-dimensional hydrodynamic flow. With the derivation of transformation hydrodynamics, the coordinate transformations for each hydrodynamic cloaking are demonstrated with the calculated viscosity tensors. The pressure and velocity fields of the square, triangular (carpet), and exemplary three-dimensional house-shaped cloaks are numerically simulated, thus showing a cloaking effect and reduced drag. This study suggests an efficient way of cloaking complex architectures from fluid-dynamic forces.     

流变岩体中让压支护作用下隧道力学行为研究

高地应力深埋软岩隧道大变形问题已成为隧道工程建设领域的突出难题. 根据高地应力深埋软岩隧道的变形特征, 基于"围岩能量吸收、变形释放"的让压支护是解决软岩隧道大变形问题的有效方法. 针对流变岩体中深埋圆形隧道在让压支护作用下的力学响应问题, 通过引入分数阶微积分理论, 采用Abel黏壶元件建立了改进的分数阶Burgers蠕变模型来表征围岩的时效变形. 此外, 通过在让压支护不同变形阶段引入刚度修正系数, 克服了传统支护未能考虑围岩变形释放的问题. 据此, 本文推导了在考虑支护延迟安装影响下, 不同变形阶段围岩与让压支护相互作用的解析解. 为了验证理论研究的正确性, 对一算例进行了不同解答及工程结果的比对, 吻合较好. 最后, 参数研究结果表明: 围岩与让压支护间的相互作用受蠕变本构模型分数阶阶数影响较大. 隧道的位移或支护压力与让压位移、支护刚度修正系数间存在线性比例关系, 但由于刚度修正系数仅保持在较小的变化范围内, 隧道的位移或支护压力变化并不显著.      

受限亚音速气流中倒置悬臂壁板静气弹稳定性的理论及实验研究

板壳结构在航空航天、高速列车、能量采集等诸多工程领域已经得到了广泛应用. 将悬臂壁板倒置于轴向气流中并在壁板周围流场中设置刚性壁面可有效地调控壁板的失稳速度, 是俘能器优化设计的重要措施之一. 但针对刚性壁面作用下亚音速气流中倒置悬臂壁板的失稳机制仍需要开展深入研究. 本文以受限亚音速气流中倒置的二维悬臂壁板为对象, 以理论分析及风洞实验为手段, 研究了单侧刚性壁面效应对倒置悬臂壁板静态失稳特性的影响规律. 在理论分析中, 首先应用镜像函数法来处理壁面约束条件, 基于算子理论研究获得了以Possio积分方程为表征的壁板气动力, 壁面效应实际表征为一包含移位Tricomi算子的复合算子; 然后将壁板失稳方程的求解问题转化为定区间上的函数逼近问题; 最后, 依据Wererstrass定理并利用最小二乘法求解该最优函数, 以获得系统的失稳临界参数. 在试验研究中依据压杆稳定原理设计了壁板静态失稳的测试方法并完成了风洞实验. 理论分析结果表明, 壁板会发生发散(静气动弹性)失稳, 临界动压随壁板与壁面间距的增加而增大并最终趋于稳定(无壁面情况); 通过理论与风洞实验结果的对比分析, 验证了本文气动力及理论分析的适用性及准确性. 针对倒置悬臂壁板结构的气动弹性失稳问题, 本文提出的方法不涉及系统方程的离散及特征值求解问题, 而是将其转化为了定区间上的函数逼近问题进行求解, 这为弹性结构静气动弹性失稳问题的研究提供了一个可行的新思路.      

基于NICE-OHMS技术进行大气压气样直接检测的理论分析

噪声免疫腔增强光外差分子光谱技术(NICE-OHMS)是目前世界上最灵敏的激光吸收光谱技术,其在低压环境中具有极高的探测灵敏度。然而当测量样品处于大气压时,NICE-OHMS系统的探测灵敏度会大幅下降。主要原因之一是大气压下获取最大NICE-OHMS信号幅度的条件与低气压下不同。通过对大气压NICE-OHMS理论进行分析,分析了影响信号幅度的参数,并通过数值模拟来寻找最佳的实验条件。本文着重讨论影响信号的主要参数包括光学腔腔长L,调制系数β,探测相位θ。其中,由于在NICE-OHMS中使用DeVoe-Brewer技术将调制频率ν_m锁定到Fabry-Parot(FP)腔的自由光谱区(FSR)。因此FP腔的腔长决定了ν_m,同时还作用于信号幅度S■。模拟结果显示,当腔长增大时,由于ν_m随之减小,载波和边带的光谱成分相互重叠部分增大,因此线型函数的幅度逐渐减小。而吸收信号幅度随着腔长的增加而逐渐增加,色散信号幅度先增大后减小,并且在腔长等于8 cm时达到最大值。调制系数β会影响频率调制后激光载波和边带的幅度大小,并且影响信号线型。随着腔长的增加,最大信号幅度对应的β值也随之增加。在相同腔长下,色散信号的最佳β值小于吸收信号,更容易使用电光调制器实现。最后分析了参数的可实现性,分析了不同种类激光器的频率调谐能力,压电陶瓷的扫描宽度等。以乙炔气体为例,大气压下NICE-OHMS的谱线半宽达到~3 GHz,而光谱覆盖范围大于10 GHz。分布反馈式半导体激光器(DFB)与外腔二极管激光器(ECDL)的频率调谐范围可以达到30 GHz以上,但是由于激光线宽宽,得到的PDH锁定性能欠佳。回音壁模式激光器(WGM)和掺饵光纤激光器(EDFL)线宽为百Hz量级,是目前高灵敏NICE-OHMS系统中常用的光源。但是WGM目前可以实现了5 GHz的激光频率调谐范围,而EDFL的外部电压可控制的调谐范围仅为3 GHz。使用精细度为55000的腔进行模拟,调制系数β=1,腔长大于8 cm时,可使用WGM激光器实现,腔长大于25 cm时,可以使用EDFL激光器实现。而对于在设计光学腔中常用的伸缩长度为25μm的PZT,随着腔长的增加,对应的腔模频移范围逐渐减小,在腔长为典型的40 cm时,扫描范围大于12 GHz。     

On the use of edge cracked short bend beam specimen for PMMA fracture toughness testing under mixed-mode I/II

In this paper an inclined edge cracked short beam specimen subjected to symmetric three-point bend loading was designed and examined for conducting mixed-mode I/II fracture toughness experiments. The aspect ratio (i.e. length to width ratio) and the loading span distance are considered much lower than the other conventional cracked bend beam samples. Crack tip parameters such as stress intensity factors and T-stress were computed numerically for this specimen by several finite element analyses and it was demonstrated that the specimen is able to produce full combinations of mode I and II including pure mode II. The practical capability of the short bend beam specimen was studied experimentally by conducting a set of mixed-mode fracture tests on PolymethylMethacrylate (PMMA) as a well-known model brittle material. The critical stress intensity factors, the direction of fracture kinking and the path of fracture trajectory were investigated both experimentally and theoretically using two stress and strain-based fracture criteria. The fracture toughness of tested PMMA was decreased by moving towards mode II case due to the effect of T-stress on the fracture mechanism of the short bend beam specimen.     

THE DEVELOPMENT OF NATIONAL ZHOU PEIYUAN COMPETITION ON MECHANICS

全国周培源大学生力学竞赛为《力学与实践》编委会发起并承办的一项大学生科技赛事,经过三十多年的发展,已经成功举办了12届,也成为展示高校力学教学水平的一个窗口。在《力学与实践》创刊40周之际,本文对全国周培源大学生力学竞赛的发展历程和组织模式进行了较为系统的回顾和梳理;对各届的组织规模和创新形式进行归纳与汇总;并通过案例说明力学竞赛对力学教学和人才培养所发挥的作用。     

Improved Reversible Zinc Storage Achieved in a Constitutionally Crystalline-Stable Mn(VO3)2 Nanobelts Cathode

Rechargeable zinc-ion batteries (ZIBs) are potential for grid-scale applications owing to their safety, low price, and available sources. The development of ZIBs cathode with high specific capacity, wide operating voltage window and stable cyclability is urgently needed in next-generation commercial batteries. Herein, we report a structurally crystalline-stable Mn(VO₃)₂ nanobelts cathode for ZIBs prepared via a facile hydrothermal method. The as-synthesized Mn(VO₃)₂ exhibited high specific capacity of 350 mAh g⁻¹ at 0.1 A g⁻¹, and maintained a capacity retention of 92 % after 10,000 cycles at 2 A g⁻¹. It also showed good rate performance and obtained a reversible capacity of up to 200 mAh g⁻¹ after 600 cycles at 0.2 A g⁻¹ under −20 °C. The electrochemical tests suggest that Mn(VO₃)₂ nanobelts impart fast Zn²⁺ ions migration, and the introduction of manganese atoms help make the structures more indestructible, leading to a good rate performance and prolonged cycle lifespan.