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.     

储箱内液体晃动动力学分析及防晃结构优化

基于光滑粒子流体动力学( SPH)方法对无阻尼板和装有阻尼板的矩形储箱在加速度激励作用下,储箱内液体的晃动与冲击进行了三维数值模拟,将测试点的计算压力及液体晃动模拟与试验进行了对比,吻合较好.从而验证了SPH方法在求解具有强非线性液体大幅晃动问题方面的准确性和优越性.分析表明:阻尼板的安装对液体的晃动特性具有显著的影响...     

液体晃动条件下飞艇水箱动力响应仿真分析

为了增加重载飞艇的载重能力,在满足结构强度要求下飞艇上的贮水水箱需要采用薄壁结构、轻质材料等方法来减轻重量。水箱在空中受到风载荷或其他载荷的作用,会导致水箱中的液体发生晃动,水箱在液体晃动和外部载荷共同作用下,可能会遭到破坏。考虑流固耦合作用对水箱结构的影响,分别从液体小幅晃动和大幅晃动两种情况对水箱动力响应进行研究。对于大幅晃动的情况,以试验所得风载荷加速度函数作为激励,利用计算流体动力学（CFD）方法进行仿真分析。分析结果表明,小幅晃动条件下,即使水箱发生共振,其结构也不会遭到破坏;大幅晃动条件下,1.3 mm以下壁厚钢材料水箱和2.1 mm以下壁厚铝合金材料水箱结构会遭到破坏。该分析结果可为水箱部分设计参数的确定提供参考依据。     

基于分段积分法的惯性系初始对准算法研究

晃动基座下无法直接根据陀螺和加速度计的输出实现方位粗对准.针对这一问题,研究了一种适用于晃动基座的初始对准新算法.该算法根据坐标系假设凝固的思想,通过坐标系分解,并采用分段积分重力矢量构造观测矢量的新方法,将初始对准姿态矩阵的求解问题转化为基于wabha问题确定对准起始时刻的姿态问题.通过利用车载实验模拟不同的晃动对准环境,验证了该算法能有效解决晃动基座下捷联惯导的初始对准问题.     

位移法浅水波方程的解及其特性

不同于传统流体力学,在Lagrange坐标下推导浅水波方程.若将水平位移作为基本变量,则推导出的浅水波数学模型可描述为固体力学的非线性大位移问题.运用不可压缩条件,通过变分原理推导出位移法浅水波方程,给出椭圆函数形式的行波解,并分析孤波解产生的条件.该基础研究建立了在分析结构力学中分析浅水波问题的理论基础,有利于进一步开展水动力学的研究.     

地震作用下非弹性地基桩的3次超谐波共振

研究了地震作用下非线性地基中桩基的3次超谐波共振问题.从地基桩中抽象出力学模型,考虑地基的非线性因素,运用Hamilton变分原理建立了桩基的非线性控制方程.利用Galerkin方法离散上述方程,基于多尺度摄动法研究了地震作用下非线性地基中桩的3次超谐波共振问题.以某嵌岩圆形桩为例,研究了地基土层厚度、剪切波速度及频率比对地震力的影响,数值模拟了非线性地基桩的3次超谐波共振响应,探讨了地震力、地基弹性及非弹性系数对超谐波幅频响应的影响,最后研究桩基产生3次超谐波共振时的时间历程曲线.结果表明,当地震波频率约等于桩基固有频率的1/3时,容易激发桩的3次超谐波共振响应;桩基的3次超谐波共振响应随着地震力、非弹性系数的增大而变得更加显著,随着弹性系数的增大而逐渐变小.     

椭圆余弦波的位移法分析

为研究线性浅水波理论的适用范围,基于位移浅水波方程的椭圆余弦波解,计算在不同水深h、波高η0和波长L条件下,非线性椭圆余弦波与线性余弦波的相对差。数值计算结果表明：η0/h越小或h/L越大,浅水波的非线性效应越弱;当η0≤0.42h且η0L2/h3≤5.34－12.85η0/h时,非线性椭圆余弦波与线性余弦波的相对差小于0.05,可满足工程需要。     

多频激励磁悬浮能量采集

研究多频激励下磁力悬浮非线性磁电能量器采集系统的动力学特性.结合谐波平衡法、牛顿迭代法和弧长延伸法近似分析非线性电力耦合的常微分方程组,研究多简谐频激励下系统的非线性稳态幅频响应特征.通过改变激励的频率,研究磁力悬浮非线性振动能量采集器的幅频特性.研究结果表明,多频激励的稳态幅频响应随非线性系数的增大而位移幅频响应的共振峰变小但带宽变宽.另外,还通过对比电学参数对共振响应幅度以及区域的影响,确定了电阻、电感和耦合系数对增强两个共振强度、扩大两个共振区域,也就是提高能量采集的强度和带宽的影响.数值模拟验证了近似解析分析结果.     

基于惯性系的旋转式惯导系统快速对准算法

针对船舶大幅角晃动和线运动等复杂干扰,导致旋转式捷联惯导系统初始对准性能下降的问题,设计了基于惯性系的旋转式捷联惯导系统快速初始对准算法.针对旋转式捷联惯导系统的误差特性,设计了基于惯性系的粗对准方案;并提出了一种改进的罗经对准算法,达到缩短对准时间和提高对准精度的目的.仿真实验证明:该方法可以实现快速初始对准,7 min航向精度达到1.35′.     

移动荷载作用下非线性基础梁内共振分析

研究了有限长弹性基础上梁在移动载荷作用下的内共振响应.建立了移动集中力激励的非线性粘弹性基础支承的有限长Euler-Bernoulli梁模型,并对非线性偏微分方程进行离散,在第三阶固有频率与第一阶固有频率成三倍关系时,采用多尺度方法导出了3:1内共振的可解性条件,研究了有无移动载荷时基础阻尼和非线性刚度对梁内共振条件下自由振动响应和受迫振动响应的影响规律.在此基础上,应用Lyapunov第一方法确定了系统的稳定性条件.     

Modeling and Simulation of Vehicles Carrying Liquid Cargo

A method for modeling and simulation of the dynamics ofvehicles subject to liquid slosh loads is presented. The vehiclecomponents are modeled as a multibody system, the sloshing liquiddynamics is determined from solving the instationary, incompressibleNavier–Stokes equations under consideration of free surfaces. Toanalyze the overall system dynamics, the concept of modular simulationis applied decomposing the dynamic system into subsystems. The rigidbody and fluid subsystems are modeled by separate software codes whichare coupled by the transfer of in- and output variables duringsimulation runtime.To account for the vehicle motions, thefluid equations of motion are transformed into a moving frame ofreference, inputs and outputs of the fluid subsystem are derived. Forsolving the incompressible Navier–Stokes equations, efficient methodshave to be applied. The system of equations resulting from a FiniteVolume discretization is solved by a multigrid method, the location offree surfaces is determined by a Volume-of-Fluid approach. To validatethe methods for modeling fluid dynamics, benchmark calculations of theflow around a cylinder and the collapse of a water column are presented.The proposed method for modeling the interaction of sloshingliquids and vehicle motions is used to determine the brakingcharacteristics of partially liquid-filled tank vehicles. It is shownthat a loss of directional control due to wheel lock-up is more likelyfor tank vehicles with sloshing liquid cargo than for vehicles loadedwith equivalent rigid cargo because of the dynamic liquid load shift.     

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．     

On the Galerkin/Finite-Element Method for the Serre Equations

A highly accurate numerical scheme is presented for the Serre system of partial differential equations, which models the propagation of dispersive shallow water waves in the fully-nonlinear regime. The fully-discrete scheme utilizes the Galerkin / finite-element method based on smooth periodic splines in space, and an explicit fourth-order Runge–Kutta method in time. Computations compared with exact solitary and cnoidal wave solutions show that the scheme achieves the optimal orders of accuracy in space and time. These computations also show that the stability of this scheme does not impose very restrictive conditions on the temporal stepsize. In addition, solitary, cnoidal, and dispersive shock waves are studied in detail using this numerical scheme for the Serre system and compared with the ‘classical’ Boussinesq system for small-amplitude shallow water waves. The results show that the interaction of solitary waves in the Serre system is more inelastic. The efficacy of the numerical scheme for modeling dispersive shocks is shown by comparison with asymptotic results. These results have application to the modeling of shallow water waves of intermediate or large amplitude.     

几种复合型数值方法的算法模拟与性能比较

浅水波问题的数值模拟一直是计算数学、计算流体力学的研究热点之一,采用低阶方法和高阶方法相复合的数值方法引起了人们的注意,并在水力学的数值模拟中取得了很大的成功。文中对三种复合型的数值方法,即Lax-Wendroff(LW)格式与Lax-Friedrichs(LF)格式的复合算法,Upwind格式与Lax-Wendroff(LW)格式的复合算法,WENO格式与LW格式的复合算法,进行了分析比较和改进,并就计算流体力学中的一维浅水波方程的两个算例分别做了数值对比试验,在解的光滑性、锐利性,计算速度等几个方面做了比较,模拟结果表明三种方法均能准确捕捉激波又不产生非物理震荡。     

基于流固耦合的非满载液罐车制动性能分析

为研究非满载充液罐车紧急制动过程中液体晃动剧烈程度,采用有限单元法对液罐车减速过程中液体晃动进行模拟.分析了相同充液比下全防波板的数量差异、相同表面积的部分防波板安装位置对液体冲击力的影响,同时,将液体压力作为负载加载到防波板上研究防波板应力变化.仿真结果得出：纵向布置的全防波板随数量的增加,可以明显降低减速过程中液体对前封头的冲击力；与相同表面积的下端防波板相比,上端防波板对降低冲击力的影响较小；将液体晃动得到的压力作为防波板载荷输入,应力最大值出现在第二块防波板处.     

A numerical investigation of errors arising in applying the galerkin method of the solution of nonlinear partial differential equations

The Galerkin method is applied to the solution of Burgers' equation and a nonlinear wave equation, using expansions of B-splines of increasing number of terms and order of spline. The accuracy of the solutions obtained numerically is compared with analytical solutions, and the effect upon accuracy of increasing the order of spline and number of terms in the expansion is considered for a variety of initial conditions corresponding to waves having a range of wavelengths.Burgers' equation is used as a model for the hydrodynamic shallow water equations, and results illustrate the importance of using a sufficient number of functions in the expansion to accurately model the distortion of a wave progressing into a shallow water region where shorter waves contribute appreciably to the total wave profile.     

Boussinesq systems in two space dimensions over a variable bottom for the generation and propagation of tsunami waves

Considered here are Boussinesq systems of equations of surface water wave theory over a variable bottom. A simplified such Boussinesq system is derived and solved numerically by the standard Galerkin-finite element method. We study by numerical means the generation of tsunami waves due to bottom deformation and we compare the results with analytical solutions of the linearized Euler equations. Moreover, we study tsunami wave propagation in the case of the Java 2006 event, comparing the results of the Boussinesq model with those produced by the finite-difference code MOST, that solves the shallow water wave equations.     

Dynamic modeling of a wave glider

We propose a method to establish a dynamic model for a wave glider, a wave-propelled sea surface vehicle that can make use of wave energy to obtain thrust. The vehicle, composed of a surface float and a submerged glider in sea water, is regarded as a two-particle system. Kane’s equations are used to establish the dynamic model. To verify the model, the design of a testing prototype is proposed and pool trials are conducted. The speeds of the vehicle under different sea conditions can be computed using the model, which is verified by pool trials. The optimal structure parameters useful for vehicle designs can also be obtained from the model. We illustrate how to build an analytical dynamics model for the wave glider, which is a crucial basis for the vehicle’s motion control. The dynamics model also provides foundations for an off-line simulation of vehicle performance and the optimization of its mechanical designs.     

Modelling coastal barrier breaching flows with well-balanced shock-capturing technique

This paper presents a coastal hydrodynamic model for simulating coastal barrier breaching flows through an inlet which are mostly induced by extreme hydrological conditions such as storm/hurricane surges, waves and tides. In order to simulate wave field and wave-induced flow field in a coast, a wave action spectral model is coupled with a hydrodynamic model. The Godunov-type shock-capturing technique is used in the hydrodynamic model to simulate the supercritical flows and shocks driven by the extreme storm conditions. The hydrodynamic model is based on the solution of depth-averaged non-linear shallow water equations with all physical forcings common to coastal hydrological conditions so that it is capable of simulating multiple flow regimes, in which subcritical, transcritical, or supercritical flows may happen. The bed slope terms in the system of equations are treated in such a way that exact balance between flux gradient and bed slope terms is achieved under still water condition. The wave model readily provides the radiation stresses that represent the shortwave-averaged forcings in a water column and take into account wave-induced nearshore currents. In the coupled system, the models are operated systematically. The coastal hydrodynamic model is shown to accurately reproduce analytical and benchmark numerical solutions. To further test the accuracy of the model, flow through a coastal inlet with a storm surge is simulated and the results are compared with an established coastal flow model. Finally, the model is examined to simulate a severe storm surge that develops supercritical flows and the results are found to be encouraging.