基于双曲面蜂窝夹层结构等效模型的研究及数值分析

蜂窝夹层结构在轻量化设计领域一直备受关注,相关的理论研究也日趋完善.然而,很多研究主要集中在平面蜂窝夹层结构上,而对于曲面结构的相关研究甚少.本文对双曲面蜂窝夹芯进行了力学分析,建立了曲面蜂窝夹层板的等效力学模型,同时建立了双曲面蜂窝夹层板详细模型和基于三明治夹层板理论以及曲面夹层板理论的等效模型,最后通过有限元方法对...     

基于非局部梁理论的嵌入式弯曲碳纳米管在移动载荷作用下的振动分析

基于非局部连续介质力学理论,针对嵌入式弯曲碳纳米管建立了两端简支的Euler-Bernoulli梁计算模型,研究碳纳米管在移动载荷作用下的非线性振动问题．利用Galerkin方法对运动微分方程进行近似处理,将原方程从非线性动力学系统转化到二阶动力学系统;对于二阶动力学方程采用Magnus级数方法进行求解;通过数值实验,分析了非局部参数因子,纳米管长径比,移动载荷速度,弯曲波纹幅值,弹性介质常数对碳纳米管振动特性的影响,结果表明上述因素对碳纳米管动力特性有很重要影响．     

Can Dirac quantization of constrained systems be fulfilled within the intrinsic geometry?

For particles constrained on a curved surface, how to perform quantization within Dirac’s canonical quantization scheme is a long-standing problem. On one hand, Dirac stressed that the Cartesian coordinate system has fundamental importance in passing from the classical Hamiltonian to its quantum mechanical form while preserving the classical algebraic structure between positions, momenta and Hamiltonian to the extent possible. On the other, on the curved surface, we have no exact Cartesian coordinate system within intrinsic geometry. These two facts imply that the three-dimensional Euclidean space in which the curved surface is embedded must be invoked otherwise no proper canonical quantization is attainable. In this paper, we take a minimum surface, helicoid, on which the motion is constrained, to explore whether the intrinsic geometry offers a proper framework in which the quantum theory can be established in a self-consistent way. Results show that not only an inconsistency within Dirac theory occurs, but also an incompatibility with Schrödinger theory happens. In contrast, in three-dimensional Euclidean space, the Dirac quantization turns out to be satisfactory all around, and the resultant geometric momentum and potential are then in agreement with those given by the Schrödinger theory.     

疲劳荷载作用下的三维弹塑性弯曲裂纹尖端张开位移

综合考虑疲劳作用应力、三维塑性区域边界上的交变正应力与交变剪应力,利用二阶摄动方法建立了计算疲劳载荷作用下三维弹塑性弯曲裂纹尖端张开位移的理论模型。用数值解法进行求解,并作图分析了三维弹塑性弯曲裂纹尖端张开位移的最大值和变化幅值与三维裂纹体几何尺寸及外载荷之间的变化关系。结果表明,随着裂纹体厚度的增大,三维弹塑性弯曲裂纹尖端张开位移的最大值与变化幅值不断减小;当裂纹体几何尺寸相同时,弯曲裂纹尖端张开位移的最大值与变化幅值均随外载荷的增加而逐渐增大。     

三维曲面腔顶盖驱动流的MRT-LBM研究

采用多松弛时间格子玻尔兹曼方法(MRT-LBM)的D3Q15模型分别对长方体腔、圆柱腔、半圆柱腔、旋转双曲面腔、旋转椭球面腔、半球腔以及两种组合腔体的三维顶盖驱动腔流进行数值模拟, 比较分析各腔体内流线分布、流速等值线分布和涡心的发展, 对于典型腔体模拟不同雷诺数下的流动情况。结果表明: 在同一雷诺数下, 曲面边界不仅能消除从边界产生的次涡, 还会导致腔内主涡的分离, 增大中心纵剖面纵向回流速度; “上长方体+下半圆柱”腔内流函数分布与边界贴合度最高。当雷诺数不断增大时, 半圆柱腔内主涡逐渐分离成两个同向涡, “上圆柱+下半球”腔内始终保持着圆柱腔与半球腔内的基本流动特征; 而长方体腔内主涡涡心保持在同一高度, 次涡逐渐增强, “上长方体+下半圆柱”腔内流动愈加规则, 主涡逐渐下沉, 流速等值线分布逐渐趋于中心小、四周大。     

Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass

In this study, a slightly curved Euler Bernoulli beam carrying a concentrated mass was handled. The beam was resting on an elastic foundation and simply supported at both ends. Effects of the concentrated mass on nonlin- ear vibrations were investigated. Sinusoidal and parabolic type functions were used as curvature functions. Equations of motion have cubic nonlinearities because of elongations during vibrations. Damping and harmonic excitation terms were added to the equations of motion. Method of mul- tiple scales, a perturbation technique, was used for solving integro-differential equation analytically. Natural frequen- cies were calculated exactly for different mass ratios, mass locations, curvature functions, and linear elastic foundation coefficients. Amplitude-phase modulation equations were found by considering primary resonance case. Effects of nonlinear terms on natural frequencies were calculated. Frequency-amplitude and frequency-response graphs were plotted. Finally effects of concentrated mass and chosen curvature function on nonlinear vibrations were investigated.     

弯曲液面上的饱和蒸气压

指出了弯曲液面上的饱和蒸气压与同温度下的饱和蒸气压之间的关系,既可依据热力学理论利用相变平衡条件求出,也可以利用毛细现象和等温气压公式求出,两者是等效的.并澄清和明确了上述关系在不同条件下可以进一步简化为不同形式.     

贵阳奥体中心体育场超大悬挑钢结构挑蓬预应力方案比较研究

贵阳奥体中心六万人体育场的看台挑篷为超大悬挑,最大悬挑近50米,采用两向斜交管桁架结构。通过沿径向上弦层外侧曲线布索施加预应力来提高结构刚度,曲线索位于悬挑一侧,且预应力索未延伸至结构的有效受力部位。对此预应力方案的效果进行初步分析,提出三种建议与改进措施;采用有限元法,对此预应力方案以及三种建议方案进行分析,对比分析各预应力方案产生的正、负效应,提出多个合理建议。     

视景仿真中液压挖掘机与地形的动态交互

液压挖掘机视景仿真系统通过采用ROAM算法动态管理和实时绘制地形网格,并利用Bezier曲面方法设定控制点的运动路径以逼近铲斗内土壤表面形状的方法,实现了液压挖掘机与三维地形的动态交互,逼真地实现了挖土和卸土效果的模拟。开发的视景仿真系统为驾驶培训人员提供了逼真的、具有高度沉浸感的虚拟内部操作场景,真实感强,具有极佳的交互性。     

前馈控制方法在非轴对称表面加工中的应用

解决非轴对称曲面的车削加工控制中压陶瓷伺服刀架的滞后问题,消除加工中的滞后误差,在分析压电陶瓷刀具迟滞缺点的基础上建立了3种消除迟滞误差的前馈控制数据模型,即：升压模型,峰值降压模型及任意点降压模型,用这些数字模型进行补偿加工实验,最大位移误差为0．05um,补偿前后的加工精度对比表明,采用前馈控制补偿的加工方法能够大大降低加工中的迟滞误差,提高非轴对称曲面的加工精度。