求旋转椭球形贮箱内液体小幅晃动基频的一种新方法

针对旋转椭球形贮箱内液体小幅晃动,建立了原点位于与箱于箱内静液面接触线处相切的圆锥的顶点的球坐标系,用高斯超几何级数解析表达速度势和波高的模态函数,通过伽辽金方法把变分方程转变为一个标准的特征值问题形式的频率方程,求解了不同尺寸比例的椭球形贮箱在不同的充液比和不同的Bond 数情况下液体小幅晃动的基频,把所求结果和已有...     

谐波平衡法求解俯仰运动矩形贮箱中液体非线性晃动

针对俯仰运动贮箱中液体的晃动用变分原理建立了一类新的Lagrange函数,以此为基础可以解析方式来研究俯仰运动贮箱中液体的非线性晃动．首先将速度势函数Φ在自由液面处作波高函数叩的Taylor级数展开,从而导出自由液面运动学和动力学边界条件非线性方程组;然后用谐波平衡法(HBM)假设其解为各次主导谐波叠加的形式,并代入方程组中得到含有未知系数相应多个代数方程式;最后用Broyden法对代数方程组求解．以无挡板开口二维、刚性矩形贮箱为例,研究了液体的大幅晃动,就液体晃动的幅值而言,在一定激励频率范围内,理论计算值与试验结果吻合较好,同时液面波高出现明显的零点漂移现象．     

充液箱位置对航天器耦合特性影响分析

分析了液体非线性晃动时充液箱位置对带弹性帆板充液航天器刚-液-弹之间耦合特性的影响.假设耦合系统绕系统质心做俯仰运动,首先采用已推导的刚-液-弹耦合系统俯仰运动非线性动力学方程组,得到系统固有频率,给出固有频率简单近似解析表达式,分析充液箱位置对系统各阶固有频率的影响.随后应用多尺度法对耦合系统液体一阶主共振进行解析分析,发现充液箱位置是决定幅频曲线软、硬特性转换点的重要参数.给定外激励力矩时,不同充液箱位置稳态解对应多解现象,并随着激励频率改变,稳态解幅值随充液箱位置的变化曲线发生分岔.     

全管理柱形表面张力贮箱设计中的强度问题

卫星推进系统的贮箱设计除需考虑静强度和外压稳定性外，随机振动和正弦振动也是卫星发射和运行中的重要环境条件，因此卫星贮箱的设计必须作动力响应计算以便对所设计结构作出安全性结论。由于贮箱内充有大量液体，表面张力管理装置大部分浸于液体中，液－固耦合的影响必需在计算中予以考虑。本文就柱形表面张力贮箱的有限元动力计算方法，建模，计算结果和对结构设计的影响加以论述。     

基于浅水波理论液体晃动初值问题的数值模拟

针对日益受到关注的液体晃动问题,提出了一种基于浅水波理论的研究方案.该方案采用浅水波理论而非势流理论导出系统控制方程,并通过哈密顿体系表达;利用中心有限差分法和Stormer-Verlet算法进行空间和时间离散;模拟了不同初值条件下的液体晃动情况并对比分析了影响系统非线性响应的主要因素.结果表明,基于浅水波理论能有效解决液体晃动问题;与Euler格式对比,Stormer-Verlet算法精度较高;除共振外对于系统非线性响应的影响容器初始位移比初始速度更显著;非共振情况一定条件下,充液容器运动过程中液体晃动能起到阻尼作用.     

基于拉格朗日描述的罐车内液体晃动模拟

基于拉格朗日描述的柔性多体系统动力学理论,采用绝对节点坐标有限元方法描述液体大变形运动,开展铁路液罐车内液体晃动模拟研究.本方法能够模拟液体自由表面的连续性变化,并适用于研究具有复杂外形容器的内部液体晃动问题.基于流体力学牛顿体基础理论,推导液体粘性方程和满足体积不可压缩的条件方程;采用基于绝对节点坐标方法描述的实体单元进行液体网格划分;采用罚函数方法描述液体与罐体之间的接触关系,组建液体-罐体耦合多体系统动力学方程.仿真计算液罐车内液体的横向和纵向晃动行为,发现液体自由表面形状呈非线性变化,不同断面处的高度和形状不同.     

全管理圆柱表面张力贮箱的微重力实验验证——静平衡与重定位

新研制的推进剂全管理柱形表面张力贮箱将工作在微重力或无重力环境下，并保证在任何时候都能向系统提供不夹气的推进剂，因而需要确定液体的空间分布以及在给定加速度过载下的重定位过程，以便为贮箱的设计提供依据，同时对推进剂管理装置进行性能验证。为此，按照相似理论用缩比的有机玻璃模型和缩比的推进剂管理装置模型进行了一系列微重力落塔实验，反映了在不同重力环境、不同液体比例、不同加载方向、不同比例模型下液体的行为     

液体晃动对飞行器控制系统影响分析

对于小幅晃动的充液飞行器流固耦合问题,可以采用等效力学模型来描述液体晃动.然而在研究液体对刚体的影响上,暂未有人从频域的角度进行建模.本文在已知液体各阶模态等效力学模型的基础上,利用虚功率原理和线性小扰动原理给出充液飞行器纵向模态舵偏角到姿态传函,并根据主导极点概念将充液飞行器高阶系统近似为二阶系统典型传递函数,以携带横放圆柱贮箱飞行器为例,分析了不同充液比和贮箱尺寸对典型传函系数的影响.结果表明,液体质量和转动惯量主要影响飞行器传递系数、时间常数,使得飞行器机动性和纵向模态自然频率降低;而液体晃动主要影响典型传函中相对阻尼系数,使得飞行器纵向相对稳定性降低.     

圆柱形贮箱液晃系统稳定性边界分析

本文研究了纵向激励下液晃系统的稳定性边界.首先利用等效摆模型获得纵向激励下液体晃动的等效动力学Mathieu方程,然后利用摄动法得到随阻尼、储液高度及贮箱直径变化时的液晃系统的稳定区域.结果表明,液体晃动阻尼、储液量及贮箱尺寸对晃动稳定性具有显著影响.     

考虑推进剂晃动的火箭液固耦合分析的比拟算法

对于弹性容器与不可压无黏液体之间的线性耦合问题,已有缩聚对称形式的液固耦合系统有限元方程.利用比拟算法获得液固耦合系统的系统矩阵,将问题转化为通用有限元程序可以解决的问题.以包含贮箱的火箭模型为例,求解火箭的模态特性,其中包括由液体晃动所引起的火箭振动模态.结果表明此类模态与重力加速度有关,频率随重力加速度的增大而增大.     

弹性支撑浅拱的非线性动力行为分析

本文研究了两端转角均为转动弹簧支撑的铰支浅拱在外激励作用下的非线性动力学行为.基于弹性支撑浅拱的基本动力控制方程,采用多尺度法对内共振进行了摄动分析,并得到了极坐标形式的平均方程.弹性约束的刚度通过特征方程影响结构的自振频率和模态,且与平均方程的相关系数一一对应,文中还以最低两阶模态之间1:1内共振为对象进行了数值分析.结果显示系统存在模态交叉与转向两种内共振形式,另一方面结构参数处于某一范围之内时外激励激发的模态作用可导致出现准周期运动和混沌运动.     

Finite element analysis of fluid-structure interaction effect on liquid retaining structures due to sloshing

Fluid-structure interaction problems, which may be categorized into different types, have attracted the attention of engineers because of their numerous practical applications. Sloshing of liquid in a liquid filled container subjected to external excitations and coupled interaction between the liquid and container wall due to sloshing is one such problem. The focus of the present paper is on the development of a numerical scheme using finite element technique to calculate the sloshing displacement of liquid and pressure developed due to such sloshing. The scheme is extended to study the coupled effect of sloshing and container wall movement due to change in the liquid pressure.     

微重环境下Cassini贮液腔中液体晃动特性研究

针对我国某一型号大型卫星液体燃料Cassini贮箱（腰为圆柱,两底为半球）,应用有限元方法研究了微重环境下液体的小幅晃动问题和横向受迫晃动问题,采用Galerkin方法得到了系统的有限元离散方程；得到了晃动固有频率和等效力学模型参数.针对周期脉冲激励,推导了液体作用于贮箱壁的晃动力和晃动力矩计算公式并给出了数值计算结果和分析结论.     

四边简支矩形薄板的双Hopf分岔分析

基于奇异性理论,研究了主参数共振-1∶3内共振情形下参数激励与外激励联合作用下四边简支矩形薄板的双Hopf分岔问题.考虑弱阻尼和弱激励的情形,得到了四边简支矩形薄板的分岔方程,给出了四边简支矩形薄板在参数平面μ-σ1上的分岔图.对参数激励与外激励联合作用下四边简支矩形薄板的阻尼系数、外激励、参数激励以及调谐参数进行不同的取值,通过数值模拟得到了四边简支矩形薄板平衡解将发生Hopf分岔,并分岔出周期解,薄板系统的非线性振动形式为周期运动.当四边简支矩形薄板的参数满足给定条件时,我们得到薄板的1∶3共振双Hopf分岔.随后,四边简支矩形薄板将会呈现概周期振动.     

Nonlinear vibration of nanobeam with attached mass at the free end via nonlocal elasticity theory

In the present study, nonlinear free and forced vibration of Euler–Bernoulli nanobeam with attached nanoparticle at the free end is investigated based on nonlocal elasticity theory. The effects of the different nonlocal parameters (γ) and mass ratios (α) as well as effects of fixed-free boundary conditions on the vibrations are determined. To obtain the equation of motion of the system, the Hamilton’s principle is employed. The stretching of neutral axis which introduces cubic nonlinearity is included into the equation for deriving nonlinear equation. And also effects of damping and forcing are included into the equations. The approximate solutions of the equations are derived by using the multiple scale method. Fundamental frequencies, frequency shift and mode shapes for the linear problem are estimated for a nonlocal Euler–Bernoulli nanobeam with an attached nanoparticle and graphically represented the frequency shift and mode shapes. Nonlinear frequencies are derived depending on amplitude and phase modulation. Frequency–response curves are drawn for different nonlocal parameters and different modes.

     

Optimal control of dual-mass system motion in a medium with a piecewise linear resistance

Linear motion of a mechanical system consisting of two bodies??a container and an inner body??is considered. The container is located in an external medium with resistance, and the inner body moves inside the container without the interaction with the external medium. Under certain conditions, the periodic motion of the inner body causes the system as a whole to move. The external medium acts on the container with a force that is proportional to its velocity with a resistance coefficient depending on the motion direction. Only the motions of the inner body with continuous relative velocity are studied. The optimal periodic motion of the inner body corresponding to the greatest period-averaged velocity of the system as a whole is constructed and analyzed.     

Periodic motion planning and control for underactuated mechanical systems

We consider the problem of periodic motion planning and of designing stabilising feedback control laws for such motions in underactuated mechanical systems. A novel periodic motion planning method is proposed. Each state is parametrised by a truncated Fourier series. Then we use numerical optimisation to search for the parameters of the trigonometric polynomial exploiting the measure of discrepancy in satisfying the passive dynamics equations as a performance index. Thus an almost feasible periodic motion is found. Then a linear controller is designed and stability analysis is given to verify that solutions of the closed-loop system stay inside a tube around the planned approximately feasible periodic trajectory. Experimental results for a double rotary pendulum are shown, while numerical simulations are given for models of a spacecraft with liquid sloshing and of a chain of mass spring system.     

Active vibration control of a fluid/plate system using a pole placement controller

We consider the problem of active reduction of the structural vibrations induced by the sloshing of large masses of fuel inside a partly full tank. The proposed study focuses on an experimental device mimicking an aircraft wing made of an aluminium rectangular plate equipped with piezoelectric patches at the clamped end and with a cylindrical tip tank, more or less filled with liquid. After deriving a representative finite-dimensional model of the complete system, containing the first five structural modes of the plate and the first three liquid sloshing modes, a controller is computed. Since our main scope is to control the most energetic mode of the structure, a full state-feedback method coupled with an observer is used. Finally, the controller is also tested for different initial conditions/perturbations and the results are compared with the ones obtained with an H _∞ controller. Experimental results illustrate the relevance of the chosen strategy.     

Capsule-type vibration-driven robot with an electromagnetic actuator and an opposing spring: Dynamics and control of motion

A model of a mobile capsule robot that consists of the housing and internal body is considered. The internal body can move relative to the housing along a straight line. The internal body is attached to the housing by a spring. The system motion is excited by a force that acts between the housing and the internal body. The force changes in a pulse-width periodic mode. The robot’s motion along a straight line on a rough horizontal plane is investigated. It is assumed that the dry Coulomb friction acts between the housing and the plane. The dependence of the average steady state robot velocity on excitation parameters is analyzed. It is established that it is possible to control the magnitude and direction of the robot motion by changing the period and the duty cycle of the pulse-width excitation signal. The effect of the variation in the direction of the robot motion due to changing the excitation period is observed. This effect is associated with the phenomenon of resonance.