Motion equations of hemispherical resonator and analysis of frequency split caused by slight mass non-uniformity

The mass non-uniformity of hemispherical resonator is one of reasons for frequency split, and frequency split can cause gyroscope to drift. Therefore, it is of great significance to analyze the relationship between mass non-uniformity and frequency split, which can provide a theoretical basis for mass balance of imperfect resonator. The starting point of error mechanism analysis for gyroscope is the motion equations of resonator. Firstly, based on the Kirchhoff-Love hypothesis in the elastic thin shell theory, the geometric deformation equations of resonator are deduced. Secondly, the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin shell. Thirdly, the kinetic energy equation of resonator is deduced by the Coriolis theorem. Finally, the motion equations of resonator are established by the Lagrange mechanics principle. The theoretical values of precession factor and natural frequency are calculated by the motion equations, which are substantially consistent with the ones by the finite element method and practical measurement, the errors are within a reasonable range. Simultaneously, the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element analysis. The above conclusions prove the correctness and rationality of motion equations. Similarly, the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping, and the state equations with respect to the velocity and displacement of vibration system are derived, then two natural frequencies are solved by the characteristic equation. It is concluded that one of reasons for frequency split is the 4th harmonic of mass non-uniformity, and thus much attention should be paid to minimizing the 4th harmonic of mass non-uniformity in the course of mass balancing for imperfect resonator.     

榫连结构的高应力梯度及破坏分析

某燕尾形榫连结构的分析表明叶盘榫齿/榫槽接触区边缘存在较高的应力梯度,接触应力的有限元解同网格疏密程度密切相关.通过建立一系列不同密度网格的模型,对此问题展开有限元建模分析,以改善接触应力的求解精度,同时深入讨论材料弹塑性对接触应力的影响.在弹塑性接触应力分析的基础上,采用断裂力学方法建立了榫连结构高应力梯度位置的破坏分析模型,判断裂纹的萌生及扩展方向,以进行结构的强度及寿命分析.     

拖靶系统飞行动力学模型研究

介绍了拖靶系统的基本组成,阐述了建立拖靶系统飞行动力学模型的意义。分别对拖机、拖靶及拖缆进行了受力分析,建立了数学模型并进行了合理假设和简化,分析了系统主要约束关系,可为拖靶系统设计及仿真研究提供参考。     

X-Cor夹层结构的平压性能

通过力学分析得到X-Cor夹层结构平压模量的解析式和计及泡沫对z-pin横向支撑的平压强度预测公式。分析X-Cor夹层结构平压模量的理论值与试验值误差,提出了结构屈曲和z-pin的长度差异引起的刚度折减的修正模型,修正后的夹层结构平压模量的理论值与试验值吻合。理论公式为X-Cor夹层结构的设计提供依据,进而为X-Cor夹层结构新材料在工程领域的应用奠定了基础。     

薄壁管壳高速正撞击穿孔特性的数值研究

受径向曲率的影响,薄壁管壳遭受高速弹丸撞击产生的局部穿孔毁伤与薄板结构并不相同。本文利用LS-DYNA3D动力学程序,采用光滑粒子流体动力学和有限元法相耦合的方法(SPH-FEM),对球形弹丸高速正撞击不同直径薄壁钢管的穿孔毁伤特性进行数值研究。根据小弹丸高速撞击薄板的物理力学性质,可把穿孔过程简化为初始流动扩孔和随后的惯性扩孔两个阶段,提出一种圆柱管壳高速正撞击穿孔的简化物理模型,并分析圆管直径对轴向孔径和径向孔径尺寸差值比的影响。数值模拟结果表明,撞击速度为2~3 km/s时,薄壁钢管的正撞击穿孔略呈椭圆状,其轴向孔径尺寸稍大于径向孔径尺寸;随着薄壁钢管直径的增加,两个方向的孔径尺寸差值比减小。另外,薄壁钢管遭受小弹丸撞击穿孔后产生碎片云的分布形态受径向直径影响明显,相同撞击条件时,钢管直径越大,则产生碎片云的膨胀角和残余速度也较大。     

The classical Laplace plane as a stable disposal orbit for geostationary satellites

The classical Laplace plane is a frozen orbit, or equilibrium solution for the averaged dynamics arising from Earth oblateness and lunisolar gravitational perturbations. The pole of the orbital plane of uncontrolled GEO satellites regress around the pole of the Laplace plane at nearly constant inclination and rate. In accordance with Friesen et al. (1993), we show how this stable plane can be used as a robust long-term disposal orbit. The current graveyard regions for end-of-life retirement of GEO payloads, which is several hundred kilometers above GEO depending on the spacecraft characteristics, cannot contain the newly discovered high area-to-mass ratio debris population. Such objects are highly susceptible to the effects of solar radiation pressure exhibiting dramatic variations in eccentricity and inclination over short periods of time. The Laplace plane graveyard, on the contrary, would trap this debris and would not allow these objects to rain down through GEO. Since placing a satellite in this inclined orbit can be expensive, we discuss some alternative disposal schemes that have acceptable cost-to-benefit ratios.     

Medium Earth Orbit dynamical survey and its use in passive debris removal

The Medium Earth Orbit (MEO) region hosts satellites for navigation, communication, and geodetic/space environmental science, among which are the Global Navigation Satellites Systems (GNSS). Safe and efficient removal of debris from MEO is problematic due to the high cost for maneuvers needed to directly reach the Earth (reentry orbits) and the relatively crowded GNSS neighborhood (graveyard orbits). Recent studies have highlighted the complicated secular dynamics in the MEO region, but also the possibility of exploiting these dynamics, for designing removal strategies. In this paper, we present our numerical exploration of the long-term dynamics in MEO, performed with the purpose of unveiling the set of reentry and graveyard solutions that could be reached with maneuvers of reasonable $\mathrm{\Delta }V$ cost. We simulated the dynamics over 120–200?years for an extended grid of millions of fictitious MEO satellites that covered all inclinations from 0 to 90°, using non-averaged equations of motion and a suitable dynamical model that accounted for the principal geopotential terms, 3rd-body perturbations and solar radiation pressure (SRP). We found a sizeable set of usable solutions with reentry times that exceed $～40$ years, mainly around three specific inclination values: 46°, 56°, and 68°; a result compatible with our understanding of MEO secular dynamics. For $\mathrm{\Delta }V?300$ m/s (i.e., achieved if you start from a typical GNSS orbit and target a disposal orbit with $e<0.3$), reentry times from GNSS altitudes exceed $～70$ years, while low-cost ($\mathrm{\Delta }V?5–35$ m/s) graveyard orbits, stable for at lest 200?years, are found for eccentricities up to $e\approx 0.018$. This investigation was carried out in the framework of the EC-funded “ReDSHIFT” project.     

浅谈工程力学课程教学改革

本文针对工程力学课程教学存在的一些问题,提出了一些改革设想.     

EPR实验结果解释述评

许多论文给出了EPR实验结果的解释。本文作者指出,EPR实验结果迫使我们修改物理学基础,并阐明这些结果蕴含着统一狭义相对论和量子力学的两条基本原理,他们是扩充的因果性原理和不可分离性原理。第一原理是狭义相对论和量子力学的共同立足点,他把因果性从类时和类光区域扩充到类空区域,第二原理是量子力学的独特性质。