机抖激光捷联惯导系统静态圆锥运动形成机理

以三轴机械抖动激光陀螺捷联惯导系统为研究对象,利用数值仿真方法,详细讨论了静态环境条件下圆锥运动的形成机理以及机械抖动激光陀螺的惯性参数对惯导系统圆锥运动的影响规律。研究认为,在静态环境条件下,惯导系统的质量分布特性不是产生圆锥运动的原因;惯导系统在静态环境条件下出现的圆锥运动是由于机械抖动陀螺抖动机构的三类不平衡——静不平衡、动不平衡和配不平衡造成的。     

结构参数对捷联惯导系统静态圆锥运动的影响

以采用整体隔振措施的配重式三轴机抖激光陀螺捷联惯导系统为研究对象,利用数值仿真方法,重点讨论了惯导系统的静不平衡、动不平衡、转动惯量以及隔振器刚度和阻尼对静态环境条件下由于陀螺抖动机构的不平衡引起的圆锥运动（细分为三类）的影响规律。研究认为,惯导系统的静平衡性和动平衡性只影响第三类圆锥运动,对一二类圆锥运动的影响甚微;惯导系统转动惯量的增大将会使圆锥运动减小;系统隔振频率越靠近陀螺抖动频率,圆锥运动越强烈;系统隔振器阻尼对圆锥运动的影响较小。研究成果可为机抖激光捷联惯导系统的结构设计及圆锥误差的事前控制提供理论指导。     

陆基导弹的无陀螺捷联惯导系统粗对准

基于一种九加速度计配置方案,给出了开平方法解算载体角速度的解算过程,并分析了无陀螺捷联惯导系统粗对准原理。由于开平方法解算角速度存在符号判断问题,所以在静基座下,系统初始对准时得不到载体角速度而导致地球自转角速度在载体坐标系上的分量无法获得。针对陆基发射导弹的无陀螺捷联惯导系统问题,提出了一种根据陆基发射导弹的初始纬度和航向角来判断载体角速度符号的方法,把此方法与开平方法解算公式结合起来可得出载体角速度矢量,进而完成陆基发射导弹无陀螺捷联惯导系统的自主式粗对准。     

等效转动矢量在捷联惯导系统二位置对准中的应用

捷联惯导系统的初始对准精度受加速度计零偏和陀螺漂移的限制。为减小对准误差,引入等效转动矢量对二位置对准方法进行了研究。通过对捷联惯导系统的静基座误差方程作Lyapunov变换,得到转动过程中加速度计零偏和陀螺漂移误差的传播方程。当系统由第一位置转到第二位置时,利用等效转动矢量的方法得到方程的状态转移矩阵,并由第一位置对准的约束条件推导出加速度计零偏和陀螺漂移的解析解。当二位置对准采用绕方位轴转动时,分析解的稳定性得出最优转动角度是180°。     

核磁共振陀螺静磁系统端口漏磁抑制技术

核磁共振陀螺作为目前世界上体积最小的导航级陀螺,受到了国内外的广泛重视。核磁共振陀螺通过检测磁场中原子核自旋进动频率的改变确定载体角速度,核磁共振陀螺的陀螺精度与静磁场的均匀性、稳定性密切相关。然而核磁共振陀螺静磁系统往往存在端口漏磁,形成杂散磁场,在长期工作过程中会磁化磁屏蔽罩,最终干扰陀螺精度。从核磁共振陀螺静磁场分布的理论分析出发,通过数学计算和计算机仿真,分析和研究了静磁系统的端口漏磁,并对静磁系统进行了优化设计。设计的核磁共振陀螺静磁系统端口漏磁在1.5倍螺线管直径范围内较传统方案平均减小45.4%,满足了核磁共振陀螺的使用需求。该工作为核磁共振陀螺仪设计和制造提供了一定的理论依据和参考价值。     

基于逆向解算的管道检测高精度定位方法

针对埋地管道检测中需要精确确定管道变形、位移等处的位置问题,提出基于逆向解算的管道检测高精度定位方法。基于惯性导航系统误差传播特性,将检测过程中惯性元件陀螺、加速计以及里程计的输出作为一个时间序列,依据检测过程中的标记点将检测过程分段,相邻两个标记点间为一段,以标记点为起始点分别做正向和逆向的导航解算,以每段的中间时刻为分割点,分别将正向解算的前二分之一数据和逆向解算的前二分之一数据作为系统的定位结果,从根本上降低系统的误差积累,提高系统的定位精度。采用实测数据将提出的方法与常用定位方法进行了比较,所提出的方法的最大定位误差为3 m,验证了方法的有效性。     

高温激波管化学非平衡流动数值模拟研究

为了预测氢氧定容燃烧驱动的高温激波管性能,需要准确分析激波管非定常化学非平衡流动过程.本文在破膜前的驱动段定容燃烧以及破膜后的化学非平衡流动数值模拟中,引入双时间步长方法,发展高温激波管化学非平衡流动数值模拟方法,该方法在时间上具有二阶精度.计算结果与目前存在的激波管流动解析解以及零维化学反应系统的数值解进行了比较,吻合较好.对于典型高温激波管状态,采用有限体积方法离散准一维流动Euler控制方程,并通过将流动过程和化学反应动力学过程耦合求解,获得了激波管内部的化学非平衡流动特征.     

基于故障树的多光纤陀螺冗余系统可靠性分析

多光纤陀螺冗余系统的可靠性分析是惯性测量系统健康状态管理中的一个关键问题.针对传统可靠性分析方法没有考虑共因失效以及在考虑共因失效后难以得到可靠度解析解的问题,提出通过一种多 Beta 因子模型描述多光纤陀螺冗余系统中的共因失效现象,并采用故障树分析方法定量评估常用多光纤陀螺冗余系统的可靠性.算例分析表明,不考虑共因失效或采用简化的共因失效模型会得到相对乐观的可靠性分析结果,从而增加系统失效的风险,因此需要采用多 Beta 因子模型.采用多 Beta因子模型后,通过故障树定量分析方法得到了典型系统可靠度的解析解,结果令人满意.     

对“应用离散算子解等离子体平衡问题”一文的商榷

本文将指出贵刊1982年第5期刊登的“应用离散算子解等离子体平衡问题”一文的不妥之处。从下面的分析看出,原文的离散方程不能描述等离子体外部解所满足的平衡方程。不能用它解环形轴对称系统中等离子体的平衡问题。     

核磁共振陀螺磁屏蔽罩内静磁场系统优化设计

核磁共振陀螺作为目前世界上体积最小的导航级陀螺,受到了国内外的广泛重视。为获得高精度与大动态范围,核磁共振陀螺通常工作在磁屏蔽罩中。根据静磁场的惟一性定理,磁力线会在磁屏蔽罩表面反射,从而影响核磁共振陀螺静磁场区域的磁场均匀性。从核磁共振陀螺静磁场分布的理论分析出发,通过数学计算和计算机仿真,分析和研究了磁屏蔽罩对静磁系统的影响,通过综合调整螺线管与屏蔽罩的交互参数,对静磁系统进行了优化设计,同时还确认了螺线管加工误差对系统性能的影响。设计的核磁共振陀螺静磁系统磁场优于1.11×10~(–5),较优化前提高至少一个数量级,满足核磁共振陀螺的使用需求。     

Internal resonance of pipes conveying fluid in the supercritical regime

This paper treats nonlinear vibration of pipes conveying fluid in the supercritical regime. If the flow speed is larger than the critical value, the straight equilibrium configuration becomes unstable and bifurcates into two possible curved equilibrium configurations. The paper focuses on the nonlinear vibration around each bifurcated equilibrium. The disturbance equation is derived from the governing equation, a nonlinear integro-partial-differential equation, via a coordinate transform. The Galerkin method is applied to truncate the disturbance equation into a two-degree-of-freedom gyroscopic systems with weak nonlinear perturbations. The internal resonance may occur under the certain condition of the supercritical flow speed for the suitable ratio of mass per unit length of pipe and that of fluid. The method of multiple scales is applied to obtain the relationship between the amplitudes in the two resonant modes. The time histories predicted by the analytical method are compared with the numerical ones and the comparisons validate the analytical results when the nonlinear terms are small.     

Coupled free vibration analysis of a fluid-filled rectangular container with a sagged bottom membrane

In the present paper, two-dimensional coupled free vibrations of a fluid-filled rectangular container with a sagged bottom membrane are investigated. This system consists of two rigid walls and a membrane anchored along two rigid vertical walls. It is filled with incompressible and inviscid fluid. The membrane material is assumed to act like an inextensible material with no bending resistance. First, the nonlinear equilibrium equation is solved and the equilibrium shape of the membrane is obtained using an analytical formulation neglecting the membrane weight. The small vibrations about the equilibrium configuration are then investigated. Along the contact surface between the bottom membrane and the fluid, the compatibility requirement is applied for the fluid–structure interactions and the finite element method is used to calculate the natural frequencies and mode shapes of the fluid–membrane system. The vibration analysis of the coupled system is accomplished by using the displacement finite element for the membrane and the pressure fluid-finite element for the fluid domain. The variations of natural frequencies with the pressure head, the membrane length, the membrane weight and the distance between two rigid walls are examined. Moreover, the mode shapes of system are investigated.     

Instability of the equilibrium state of a liquid with a free surface in the presence of volume heat sources

The problem of the convection of a weakly compressible fluid is considered. In the free convection equations a heat source function is taken into account. The stability of the equilibrium state of a horizontal layer relative to small perturbations is studied using the linearization method. On the basis of numerical calculations it is shown that the mechanical equilibrium state of the fluid is unstable. The neutral curves are plotted and the critical Rayleigh numbers are found. In the calculations values of the physical parameters typical of Lake Baikal were used.     

饱和多孔介质大变形分析的一种有限元-有限体积混合方法

建立了饱和多孔介质大变形分析的一种有限元-有限体积混合计算方法.将饱和多孔介质视为由固体骨架和孔隙水组成的两相体,其基本方程包括动力平衡方程和渗流连续方程.基于u-p假定和更新的Lagrange方法,饱和多孔介质的动力平衡方程在空间域内采用有限元方法进行离散,而渗流连续方程在空阃域内则采用有限体积法进行离散.通过两个数值算例,一维有限弹性固结和动力荷载作用下堤坝动力响应的计算,验证了该方法的有效性.     

HOPF BIFURCATION OF A NONLINEAR RESTRAINED CURVED PIPE CONVEYING FLUID BY DIFFERENTIAL QUADRATURE METHOD

This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support. The nonlinear equation of motion is derived by forces equilibrium on microelement of the system under consideration. The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is solved by the Newton-Raphson method. The numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter,nonlinear spring stiffness. Based on this, the cycle and divergent motions are both found to exist at specific fluid flow velocities with a given value of the nonlinear spring stiffness. The results are useful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.     

微重时卧圆柱内静液面方程与数值计算

由力学平衡方程导出了微重时卧圆柱内静液面方程，推出了边界接触角条件，使用Ｒｕｎｇｅ Ｋｕｔａ法在计算机上得出了数值结果，绘出了静液面形状，并对结果进行了分析．     

Nonlinear dynamics of functionally graded pipes conveying hot fluid

For improved stability of fluid-conveying pipes operating under the thermal environment, functionally graded materials (FGMs) are recommended in a few recent studies. Besides this advantage, the nonlinear dynamics of fluid-conveying FG pipes is an important concern for their engineering applications. The present study is carried out in this direction, where the nonlinear dynamics of a vertical FG pipe conveying hot fluid is studied thoroughly. The FG pipe is considered with pinned ends while the internal hot fluid flows with the steady or pulsatile flow velocity. Based on the Euler–Bernoulli beam theory and the plug-flow model, the nonlinear governing equation of motion of the fluid-conveying FG pipe is derived in the form of the nonlinear integro-partial-differential equation that is subsequently reduced as the nonlinear temporal differential equation using Galerkin method. The solutions in the time or frequency domain are obtained by implementing the adaptive Runge–Kutta method or harmonic balance method. First, the divergence characteristics of the FG pipe are investigated and it is found that buckling of the FG pipe arises mainly because of temperature of the internal fluid. Next, the dynamic characteristics of the FG pipe corresponding to its pre- and post-buckled equilibrium states are studied. In the pre-buckled equilibrium state, higher-order parametric resonances are observed in addition to the principal primary and secondary parametric resonances, and thus the usual shape of the parametric instability region deviates. However, in the post-buckled equilibrium state of the FG pipe, its chaotic oscillations may arise through the intermittent transition route, cyclic-fold bifurcation, period-doubling bifurcation and subcritical bifurcation. The overall study reveals complex dynamics of the FG pipe with respect to some system parameters like temperature of fluid, material properties of FGM and fluid flow velocity.     

The Onset of Double-Diffusive Convection in a Superposed Fluid and Porous Layer Under High-Frequency and Small-Amplitude Vibrations

We numerically simulate the initiation of an average convective flow in a system composed of a horizontal binary fluid layer overlying a homogeneous porous layer saturated with the same fluid under gravitational field and vibration. In the layers, fixed equilibrium temperature and concentration gradients are set. The layers execute high-frequency oscillations in the vertical direction. The vibration period is small compared with characteristic timescales of the problem. The averaging method is applied to obtain vibrational convection equations. Using for computation the shooting method, a numerical investigation is carried out for an aqueous ammonium chloride solution and packed glass spheres saturated with the solution. The instability threshold is determined under two heating conditions—on heating from below and from above. When the solution is heated from below, the instability character changes abruptly with increasing solutal Rayleigh number, i.e., there is a jump-wise transition from the most dangerous shortwave perturbations localized in the fluid layer to the long-wave perturbations covering both layers. The perturbation wavelength increases by almost 10 times. Vibrations significantly stabilize the fluid equilibrium state and lead to an increase in the wavelength of its perturbations. When the fluid with the stabilizing concentration gradient is heated from below, convection can occur not only in a monotonous manner but also in an oscillatory manner. The frequency of critical oscillatory perturbations decreases by 10 times, when the long-wave instability replaces the shortwave instability. When the fluid is heated from above, only stationary convection is excited over the entire range of the examined parameters. A lower monotonic instability level is associated with the development of perturbations with longer wavelength even at a relatively large fluid layer thickness. Vibrations speed up the stationary convection onset and lead to a decrease in the wavelength of most dangerous perturbations of the motionless equilibrium state. In this case, high enough amplitudes of vibration are needed for a remarkable change in the stability threshold. The results of numerical simulation show good agreement with the data of earlier works in the limiting case of zero fluid layer thickness.     

Effect of a permeable partition on convective instability in a rectangular cavity

The equilibrium stability of a fluid, heated from below, in a rectangular cavity with a vertical permeable partition is investigated. The small perturbation problem is solved by the Galerkin-Kantorovich method. The relations obtained for the dependence of the critical Rayleigh numbers on the partition parameters and the cavity dimensions make it possible to identify regions in which either even or odd perturbations, sensitive to only the normal or only the tangential resistance of the partition, respectively, are responsible for equilibrium crisis. The effect of a permeable partition on the convective instability of a horizontal layer of fluid under various heating conditions was considered in [1–3], where a significant dependence of the critical Rayleigh numbers on the properties of the partition was established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 6–10, May–June, 1989.