柱面微通道板的制备及其性能研究

针对未来空间天文学应用的超分辨率光谱成像仪器的需求，对低噪声柱面微通道板（MCP）的制备方法及其性能进行了研究. 提出了一种将光学抛光与热成型相结合的新的柱面MCP制备方法，利用不含放射性元素的低噪声MCP玻璃，制备出曲率半径为400mm、尺寸为30mm′46mm、长径比为80:1、通道直径12.5mm、通道间距15mm的柱面MCP，并将其与感应电荷楔条形阳极（WSA）组成光子计数探测器，对其暗计数率、分辨率进行了检测，暗计数率约为0.1counts/cm2×s.     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

借助空间向量速求立体几何中的距离

空间向量的引入,有效降低了立体几何问题的思维难度,使有关问题的求解程序化.高考对立体几何的考查,侧重于位置关系与数量关系,而数量关系中的"距离"问题主要有:两点间距离;点线距离;点面距离;线线(异面直线)距离;平行线面的距离;平行的面面距离等,其中,两点之间距离、点线的距离易求,线面距离、面面距离都可转化为点面距离,本文例析借助空间向量,快速求解立体几何中的两种距离:异面直线之间的距离和点到平面的距离.     

四边简支功能梯度圆锥壳的非线性振动分析

研究了四边简支条件下功能梯度圆锥壳的非线性自由振动。首先,通过Voigt模型和幂律分布模型描述了功能梯度材料的物理属性。然后,考虑von-Karman几何非线性建立了功能梯度圆锥壳的能量表达式,利用Hamilton原理推出圆锥壳的运动方程。在此基础上,采用Galerkin法,只考虑横向振动,功能梯度圆锥壳运动方程可简化为单自由度非线性振动微分方程。最后,通过改进的L-P法和Runge-Kutta法求解非线性振动方程,讨论功能梯度圆锥壳的非线性振动响应,分析几何参数和陶瓷体积分数指数对圆锥壳非线性频率响应的影响。结果表明,几何参数对非线性频率和响应的影响相较于陶瓷体积分数指数更明显;圆锥壳的几何参数和陶瓷体积分数指数通过改变非线性频率影响振动响应;功能梯度圆锥壳呈弹簧渐硬非线性振动特性。     

含双裂纹圆截面悬臂梁的损伤识别研究

裂纹的萌生和扩展直接影响构件的振动响应，对构件的安全可靠性具有重要影响．本文以圆截面悬臂梁为对象，结合转角模态振型和模态频率等高线，研究了一种双裂纹识别技术．首先，基于应力强度因子和卡氏定理推导了无裂纹梁单元和含裂纹梁单元的刚度矩阵；在此基础上，建立了含裂纹圆截面悬臂梁的有限元动力学方程；然后，结合裂纹对梁转角模态振型和模态频率的影响，提出了双裂纹识别策略．最后，通过算例讨论了双裂纹识别策略的可行性．结果表明，圆截面悬臂梁的模态转角在裂纹位置出现突变，裂纹深度越大转角突变值越大；将识别出的裂纹位置作为已知参数，通过模态频率等高线法，可以准确地识别出双裂纹的深度．     

单向双筋板结构件共振疲劳试验及分析

航空航天领域广泛存在着振动疲劳问题,严重危及飞行器结构的安全可靠性。本文首先设计了激振器直接作用于试件的力激励振动疲劳试验系统,并提出了跟踪结构共振频率的频带激励共振疲劳寿命测试方法;而后利用试件进行了频带激励下的定应变共振或定载荷共振结构振动疲劳试验;最后针对试验结果分析与讨论了可能影响结构振动疲劳寿命的各种因素。结论表明,试验结构件的边界条件、初始条件以及结构动力学特性等都可能是影响振动疲劳寿命的关键因素。频带激励共振疲劳试验方法为振动疲劳寿命曲线的测试积累了经验。