PIMOL: The Finite Difference Method of Lines Based on the Precise Integration Method for an Arbitrary Irregular Domain

The aim of this paper is to introduce a new semi-analytical method named precise integration method of lines(PIMOL),which is developed and used to solve the ordinary differential equation(ODE)systems based on the finite difference method of lines and the precise integration method.The irregular domain problem is mainly discussed in this paper.Three classical examples of Poisson^equation problems are given,including one regular and two irregular domain examples.The PIMOL reduces a semi-discrete ODE problem to a linear algebraic matrix equation and does not require domain mapping for treating the irregular domain problem.Numerical results show that the PIMOL is a powerful method.

IMPLICITY LINEAR COLLOCATION METHOD AND ITERATED IMPLICITY LINEAR COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF HAMMERSTEIN FREDHOLM INTEGRAL EQUATIONS ON 2D IRREGULAR DOMAINS

In this work,we adapt and compare implicity linear collocation method and iterated implicity linear collocation method for solving nonlinear two dimensional Fredholm integral equations of Hammerstein type using IMQ-RBFs on a non-rectangular domain.IMQs show to be the most promising RBFs for this kind of equations.The proposed methods are mesh-free and they are independent of the geometry of domain.Convergence analysis of the proposed methods together with some benchmark examples are provided which support their reliability and numerical stability.

An Indirect-Forcing Immersed Boundary Method for Incompressible Viscous Flows with Interfaces on Irregular Domains

An indirect-forcing immersed boundary method for solving the incompressible Navier-Stokes equations involving the interfaces and irregular domains is developed.The rigid boundaries and interfaces are represented by a number of Lagrangian control points.Stationary rigid boundaries are embedded in the Cartesian grid and singular forces at the rigid boundaries are applied to impose the prescribed velocity conditions.The singular forces at the interfaces and the rigid boundaries are then distributed to the nearby Cartesian grid points using the immersed boundary method.In the present work,the singular forces at the rigid boundaries are computed implicitly by solving a small system of equations at each time step to ensure that the prescribed velocity condition at the rigid boundary is satisfied exactly.For deformable interfaces,the forces that the interface exerts on the fluid are computed from the configuration of the elastic interface and are applied to the fluid.The Navier-Stokes equations are discretized using finite difference method on a staggered uniform Cartesian grid by a second order accurate projection method.The ability of the method to simulate viscous flows with interfaces on irregular domains is demonstrated by applying to the rotational flow problem,the relaxation of an elastic membrane and flow in a constriction with an immersed elastic membrane.

Parallel Molecular Dynamics with Irregular Domain Decomposition

The spatial domain of Molecular Dynamics simulations is usually a regular box that can be easily divided in subdomains for parallel processing.Recent efforts aimed at simulating complex biological systems,like the blood flow inside arteries,require the execution of Parallel Molecular Dynamics(PMD)in vessels that have,by nature,an irregular shape.In those cases,the geometry of the domain becomes an additional input parameter that directly influences the outcome of the simulation.In this paper we discuss the problems due to the parallelization of MD in complex geometries and show an efficient and general method to perform MD in irregular domains.

高速铁路0.01~1 m波段高低轨道不平顺特性分析

随着我国高速铁路发展规模的不断扩大及运营速度的不断提升,轨道短波不平顺引起的振动与噪声问题日益严重。深入研究高速铁路短波不平顺的时域、频域与时频域特征,对精准掌握高速铁路轨道短波平顺状态及其引起的车-轨系统振动、伤损等一系列问题具有重要的参考价值。以某高速铁路实测0.01~1 m波段轨面高低不平顺数据为研究对象,经过数据预处理剔除异常值并消除趋势项后,对实测不平顺数据进行时域分析,得到该高铁线路短波不平顺数据的统计与分布特性。采用平均周期图法计算该高铁线路轨道短波不平顺功率谱密度,应用非线性最小二乘拟合优化算法进行拟合,提出高速铁路轨道短波不平顺谱。从时频域角度对该段数据进行经验模态分解与希尔伯特变换,分析该高铁线路短波不平顺的希尔伯特谱与边际谱。研究结果表明:该高铁线路轨道短波不平顺数据各统计量幅值都较小,且近似服从正态分布;该高铁线路轨道短波不平顺功率谱密度存在与钢轨波磨有关的多个周期性成分,提出的高速铁路短波不平顺谱函数能够很好地对实测功率谱密度进行拟合,且拟合效果优于经典的SATO建议的短波谱与50 kg/m钢轨的短波谱;对该高铁线路轨道可能存在的短波病害进行识别与定位,时频域分析的方法可以较好地应用于高速铁路轨道平顺性的分析与日常的管理维护。

考虑时变特性的车-桥耦合系统非平稳振动频域方法研究

当列车行驶经过桥梁时,由于车辆在桥上的位置随时间不断变化,车-桥耦合系统具有时变特性,即使假设轨道不平顺为平稳激励,车辆和桥梁的振动仍然是一种非平稳的随机过程。本研究旨在提出一种非平稳频域分析方法,以高效分析受轨道不平顺激励的车-桥耦合系统的非平稳随机振动问题。首先推导了单节列车通过单跨简支桥的耦合系统时变频响传递函数(FRF),据此描述线性时变系统的动力特性。该函数满足一组变系数微分方程,可采用摄动法求解该函数,从而提高计算效率。随后,结合PRIESTLEY的演化谱理论,推导非平稳随机响应的演化功率谱密度函数(EPSD)。基于非平稳频域分析方法,计算响应时变均值和方差,结合3σ准则来估计非平稳响应的极值。研究结果表明,由于轨道不平顺的影响,车辆振动表现出平稳随机过程的特性,但其方差较大,表现出更大的离散性;而桥梁的振动则呈现出明显的非平稳特性,但方差较小,响应具有较小的随机性。极值分析表明,轨道不平顺激励对车辆振动具有显著影响,其均方根对极值响应起主导作用。而轨道不平顺激励对桥梁振动的影响较小,桥梁振动则主要受移动质量影响,其响应的极值主要受均值的影响。此外,相较于系统位移响应,车速对加速度响应的影响更为显著,例如车身加速度响应最大值随车速的增加可增大至3倍左右。

防沉板结构吊装入水作业动力学时域仿真

针对防沉板结构物吊装入水作业中吊绳拉力和结构物运动响应问题,建立钢制防沉板、水下分布单元和管汇离散为圆柱的吊装入水时域模型。依据规则波吊装入水作业吊绳拉力结果确定防沉板结构入水过程中危险吊装状态的范围。进一步通过不同悬停吊装下不规则波的砰击,分析拉力的动态响应,确定防沉板结构物吊装的最危险状态。研究最危险状态下吊绳拉力动态放大因子和水动力随不规则波的时域和频域变化规律。结果表明,钢制防沉板的裙板浸没0.2 m附近时的状态最危险,此时吊绳的动态响应最大。在最危险状态下,吊绳拉力的动态响应更容易受到波高的影响,且分吊绳的动态放大因子比主吊绳更小,所以分吊绳最可能发生松弛。

Response Analysis of Tension-Based Tension Leg Platform Under Irregular Waves

Tension Leg Platform（TLP） is a hybrid structure used as oil drilling and production facility within water depths of 1200 m. The extension of this TLP concept to deeper waters is a challenge and warrants for some innovative design concepts. In this paper, a relatively new concept of TLP which is christened as Tension-Based Tension Leg Platform（TBTLP） and patented by Srinivasan（1998） has been chosen for study. Response analysis of TLP with one tension base under irregular waves for three different sea states has been performed using hydrodynamic tool ANSYS？ AQWA？. Results are reported in terms of RAOs, response spectrums for surge, heave and pitch degrees of freedom from which spectral statistics have been obtained. The statistics of TBTLP have been compared with TLPs（without tension base） for two different water depths to highlight the features of the new concept. The effect of viscous damping and loading effects on the RAOs are also investigated.

A local refinement purely meshless scheme for time fractional nonlinear Schrodinger equation in irregular geometry region

A local refinement hybrid scheme(LRCSPH-FDM)is proposed to solve the two-dimensional(2D)time fractional nonlinear Schrodinger equation(TF-NLSE)in regularly or irregularly shaped domains,and extends the scheme to predict the quantum mechanical properties governed by the time fractional Gross-Pitaevskii equation(TF-GPE)with the rotating Bose-Einstein condensate.It is the first application of the purely meshless method to the TF-NLSE to the author’s knowledge.The proposed LRCSPH-FDM(which is based on a local refinement corrected SPH method combined with FDM)is derived by using the finite difference scheme(FDM)to discretize the Caputo TF term,followed by using a corrected smoothed particle hydrodynamics(CSPH)scheme continuously without using the kernel derivative to approximate the spatial derivatives.Meanwhile,the local refinement technique is adopted to reduce the numerical error.In numerical simulations,the complex irregular geometry is considered to show the flexibility of the purely meshless particle method and its advantages over the grid-based method.The numerical convergence rate and merits of the proposed LRCSPH-FDM are illustrated by solving several 1D/2D(where 1D stands for one-dimensional)analytical TF-NLSEs in a rectangular region(with regular or irregular particle distribution)or in a region with irregular geometry.The proposed method is then used to predict the complex nonlinear dynamic characters of 2D TF-NLSE/TF-GPE in a complex irregular domain,and the results from the posed method are compared with those from the FDM.All the numerical results show that the present method has a good accuracy and flexible application capacity for the TF-NLSE/GPE in regions of a complex shape.

Multiresolution method for bending of plates with complex shapes

A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.

基于振动台试验的加速度积分位移

轨道不平顺是铁路车辆系统振动的主要激励源,车体构架运行姿态的变化会对轨道几何不平顺检测精度造成影响.理论上可通过位移传感器对车体构架的运行姿态进行测试,但多数情况下测量困难且精度较低,而采用加速度传感器测试,又存在各种噪声干扰,使积分位移中含有趋势项漂移误差.针对此类问题,提出了一种从加速度数据中获取位移时间序列的低频衰减频域积分方法.该方法从测量加速度积分开始,采用基于滑动平均的最小二乘法预处理方法,去除积分过程中的噪声产生的误差,还原实际由于轨道不平顺产生的振动响应.结合滑动平均方法、高通滤波器和频域积分,通过多次平滑、滤波和积分,得到重构位移信号,避免了信号的失真.该方法的主要优点是重构位移不存在长周期漂移.通过与振动台实测数据的对比分析,验证了该方法的准确性和可靠性.

轨道随机不平顺对地铁振动源强时-频特性影响的仿真研究

目的:为了探究轨道的多种随机不平顺(高低、水平、轨距和轨向)在不同列车速度下对地铁隧道壁垂向振动加速度和轮轨力的影响,以提升行车品质,特进行本研究。方法:以地铁A型车为例,运用动力学分析软件建立考虑柔性轮对的车辆刚柔耦合系统动力学模型。将轨道和轮对视为柔性体,其余部件视为刚体,通过施加多种随机不平顺和改变车辆速度并考虑波磨来模拟不同工况,进行仿真计算。同时采用快速傅里叶变换方法对仿真计算结果进行时域和频域分析,研究隧道壁和轮轨力的振动特性。结果及结论:研究结果表明:随着车辆运行速度的增大,隧道壁垂向振动加速度的峰值有所提高,优势频率分布范围会有稍许扩大,高频成分增多;车轮间相互作用加剧,垂向轮轨力有所增大;隧道壁在4~200 Hz范围内的振动主频为63 Hz,不随速度变化而变化,但加速度级峰值会有所增大。

新型160 km/h铁路货运棚车车门疲劳寿命研究

在车辆运行过程中,由于轨道不平顺或随机风载的影响,车体会持续受到随机振动载荷的影响,严重时会对车体结构产生疲劳破坏。为保证运行安全,对某新型160 km/h大容积全侧开活动侧墙棚车车门进行随机振动疲劳分析。考虑到转向架、车体等零部件在激励传递过程中的影响,通过柔性建模方法建立车体动力学模型,选用美国6级线路谱进行仿真,提取出车门垂向振动加速度谱,分别运用基于应力响应功率谱密度函数的频域分析法和基于雨流计数法的时域分析法对车门疲劳损伤进行计算。结果表明,2种算法计算的车门疲劳寿命都满足600万km的运营需求,并且疲劳强度薄弱区域都显示为车门座焊接部位,其中频域分析法计算的疲劳损伤值为0.89,时域分析法计算的疲劳损伤值为0.51,前者更为保守,最后从数据处理方式、评估方法、算法原理3个方面分析了2种计算结果的差异原因。

波浪反射系数计算方法的性能分析

由于噪声和非线性等因素的干扰,波浪场中波浪反射系数的计算精度会受到不同程度的影响,为了在复杂海况中准确地计算反射系数,需要对各算法的精确度和稳定性进行系统研究和分析。本文将噪声项和非线性成分叠加到简谐波中合成符合实际情况的规则波和不规则波;运用各种算法对不同预设反射率的波况进行计算并比较其性能参数;将各方法进一步应用于物理波浪水槽反射系数的计算,再次验证各算法的性能。通过对比最优间距下的计算结果发现,在规则波中,Mansard三点法、Goda两点法和传递函数法性能优于其他算法;在不规则波中,Goda两点法计算频率范围受限,传递函数法分离反射波误差较大,Mansard三点法性能表现最优。本文的研究可为不同波况下反射系数的计算提供理论参考,在模型试验及工程应用中具有一定的实践指导意义。

便携式轨检仪轨道中短波高低不平顺检测方法研究

根据便携式轨检仪解算轨道高低不平顺的原理,推导出姿态角解算轨道高低不平顺的有效波长范围。针对姿态角在中短波范围解算的不足,在便携式轨检仪中安装加速度计。参照轴箱加速度积分法原理,建立了轨道高低不平顺激励的车-轨耦合模型,分析了波长和车速对轴箱加速度解算精度的影响,结合仿真结果,提出基于轴箱加速度的轨道中短波高低不平顺检测方法,包括时域积分算法、趋势项消除方法、粗误差消除方法。为验证该方法的准确性,应用GCYⅡ-300型轨道车在准池铁路高家堡站—八里铺站进行了现场试验。采用上述方法对实测数据进行处理,得到试验区间轨道的高低不平顺幅值大部分在±10 mm以内,最高峰值为12 mm,与轨检数据近似。研究结果表明,在中短波范围内,轴箱垂向加速度可以准确反映轨道高低不平顺特征,便携式轨检仪检测精度满足相关技术要求。

线路不平顺波长对提速列车横向舒适性影响

为提高列车在提速区段的乘坐舒适性,借助于现场试验测试数据,运用车辆-轨道耦合动力学理论,通过轨道随机不平顺功率谱变换得到不同波长的不平顺,研究了线路不平顺波长对列车运行平稳性及乘坐舒适性的影响及规律。分析结果表明:提速机车以150km.h-1速度在直线轨道上运行时,如果线路不平顺波长为1～20m,则车体振动主频主要集中在2.20～4.00Hz,避开了人体正常敏感频率,平稳性指标属优级;如果线路不平顺波长为20～30m,则车体振动主频降低至1.50Hz左右,正好处于人体敏感频率范围,乘坐舒适性大大降低,平稳性指标值增加了20%多;更长的波长(大于30m)对机车运行平稳性影响较小,指标与1～20m波长的相应值处于相同等级。可见,对于既有提速线路,必须严格控制不平顺的20～30m波长,虽然该波段的不平顺幅值很小,但对列车在提速区段车体横向振动影响甚大。

不规则区域热传导问题无网格Petrov-Galerkin方法的数值模拟

无网格Petrov-Galerkin(MLPG)方法是一种真正的无网格方法,它利用节点计算待求量的插值函数,并利用高斯型求积公式在局部子域内进行数值积分。本文提出了一种有效的用于不规则区域的高斯型数值积分实施方法,通过数值研究表明:该方法能很好地处理不规则区域积分,其计算结果与基准解和FLUENT的计算结果吻合很好。

基于多弦模型的轨道短波不平顺测量研究

弦测是目前铁道工务中对钢轨不平顺检查广泛使用的一种手段,但理论上的缺陷制约了其对较短波长的响应。在分析中点弦测法频域特性的基础上,提出了多弦测量理论及数据补偿方法。根据不平顺波段的不同找到合适的弦长组合避免了幅值增益为零;利用傅里叶变换在频域对测量结果进行补偿可得到原始值。数据仿真及实际线路测试结果表明,该方法能够准确的计算出轨道短波不平顺幅度,适合工程中的应用。

无网格局部强弱法求解不规则域问题

无网格局部彼得洛夫-伽辽金(meshless local Petrov-Galerkin,MLPG)法是一种具有代表性的无网格方法,在计算力学领域得到广泛应用.然而,这种方法在边界上需执行积分运算,通常很难处理不规则求解域问题.为了克服MLPG法的这种局限性,提出了无网格局部强弱(meshless local strong-weak,MLSW)法.MLSW法采用MLPG法离散内部求解域,采用无网格介点(meshless intervention-point,MIP)法施加自然边界条件,并采用配点法施加本质边界条件,避免执行边界积分运算,可适用于求解各类复杂的不规则域问题.从理论上讲,这种结合式方法,既保持了MLPG法稳定而精确计算的优势,同时兼备配点型方法在处理复杂结构问题时简洁而灵活的优势,实现了弱式法和强式法的优势互补.此外,MLSW法采用移动最小二乘核(moving least squares core,MLSc)近似法来构造形函数,是对传统移动最小二乘(moving least squares,MLS)近似法的一种改进.MLSc使用核基函数代替通常的基函数,有利于数值求解的精确性和稳定性,而且其导数近似计算变得更为简单.数值算例结果初步表明:这种新方法实施简单,求解稳定、精确,表现出适合工程运用的潜力.

车辆道路模拟的计算机仿真系统设计研究(英文)

为了对道路随机激励下车辆的平顺性动力学进行研究首先必须建立道路高程的时间历程。为了对时域内道路的数学模型、算法设计和道路仿真实现的研究,分析了道路不平顺高程从频域向时域的转换方法并在建模数值道路过程中考虑了车轮之间以及两轮辙之间的相关性,设计了三种主要的道路模拟算法——谐波叠加法、白噪声过滤法和基于道路功率谱离散的逆Fourier变换法并将其于MATlab平台上集成为专用的道路仿真系统。为使仿真尽可能真实,包括时域中的双轮辙关系、道路仿真算法的改进以及多元算法的集成等方面也给予了重视。仿真算例研究表明了所用方法原理上的普适性、有效性,以及仿真结果与实际道路的一致性。