Simulation of anchor chain based on lumped mass method

In order to develop a anchoring operation simulation system and improve safety during anchoring operations,a relatively accurate mathematical model of anchoring operations needs to be established.In this paper,the stress condition of anchor chain under environmental and subsea geological conditions is further studied and the stress condition of anchor chain is analyzed based on the previous research.In this paper,a quasi-static model based on catenary method is used as the basis of dynamic analysis,and the dynamic model of anchor chain is established based on the concentrated mass method,which fully considers the influence of anchor chain weight,hydrodynamic force,ocean current and interaction with the seabed.The fourth-order Runge Kutta method was used to solve the model numerically,and a calculation procedure was developed.The accuracy of the model was verified by comparing the calculated results with the experimental results,indicating that the constructed anchor chain dynamics model has a high accuracy.

A lumped mass nonconforming finite element method for nonlinear parabolic integro-differential equations on anisotropic meshes

A lumped mass approximation scheme of a low order Crouzeix-Raviart type noncon- forming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.

Modal analysis on transverse vibration of axially moving roller chain coupled with lumped mass

The modal characteristics of the transverse vibration of an axially moving roller chain coupled with lumped mass were analyzed.The chain system was modeled by using the multi-body dynamics theory and the governing equations were derived by means of Lagrange's equations.The effects of the parameters,such as the axially moving velocity of the chain,the tension force,the weight of lumped mass and its time-variable assign position in chain span,on the modal characteristics of transverse vibration for roller chain were investigated.The numerical examples were given.It is found that the natural frequencies and the corresponding mode shapes of the transverse vibration for roller chain coupled with lumped mass change significantly when the variations of above parameters are considered.With the movement of the chain strand,the natural frequencies present a fluctuating phenomenon,which is different from the uniform chain.The higher the order of mode is,the greater the fluctuating magnitude and frequency are.

A lumped mass Chebyshev spectral element method and its application to structural dynamic problems

A diagonal or lumped mass matrix is of great value for time-domain analysis of structural dynamic and wave propagation problems,as the computational efforts can be greatly reduced in the process of mass matrix inversion.In this study,the nodal quadrature method is employed to construct a lumped mass matrix for the Chebyshev spectral element method(CSEM).A Gauss-Lobatto type quadrature,based on Gauss-Lobatto-Chebyshev points with a weighting function of unity,is thus derived.With the aid of this quadrature,the CSEM can take advantage of explicit time-marching schemes and provide an efficient new tool for solving structural dynamic problems.Several types of lumped mass Chebyshev spectral elements are designed,including rod,beam and plate elements.The performance of the developed method is examined via some numerical examples of natural vibration and elastic wave propagation,accompanied by their comparison to that of traditional consistent-mass CSEM or the classical finite element method(FEM).Numerical results indicate that the proposed method displays comparable accuracy as its consistent-mass counterpart,and is more accurate than classical FEM.For the simulation of elastic wave propagation in structures induced by high-frequency loading,this method achieves satisfactory performance in accuracy and efficiency.

New lumped-mass-stick model based on modal characteristics of structures: development and application to a nuclear containment building

In this study, a new lumped-mass-stick model （LMSM） is developed based on the modal characteristics of a structure such as eigenvalues and eigenvectors. The simplified model, named the ＂frequency adaptive lumped-massstick model,＂ hasonly a small number of stick elements and nodes to provide the same natural frequencies of the structure and is applied to a nuclear containment building. To investigate the numerical performance of the LMSM, a time history analysis is carried out on both the LMSM and the finite element model （FEM） for a nuclear containment building. A comparison of the results shows that the dynamic responses of the LMSM in terms of displacement and acceleration are almost identical to those of the FEM. In addition, the results in terms of floor response spectra at certain elevations are also in good agreement.

Lumped Parameter Mass Flow Rate and Pressure Control Characteristics Model for High-Speed Pneumatic PWM on/off Valve

Aiming at solving the problem of strong coupling characteristic of the key parameters of high-speed pneumatic pulse width modulation( PWM) on / off valve, a general lumped parameter mathematical model based on the valves time periods was well developed. With this model,the mass flow rate and dynamic pressure characteristics of constant volumes controlled by high-speed pneumatic PWM on /off valves was well described. A variable flow rate coefficient model was proposed to substitute for the constant one used in most of the prior works to investigate PWM on /off valves' dynamical pressure response, and a formula for disclosing the inherent relationship among the PWM command signal,static mass flow rate,and sonic conductance of the valve was newly derived.Finally,an extensive set of analytical experimental comparisons were implemented to verify the validity of the proposed mathematica model. With the proposed model, PWM on /off valves' characteristics,such as mass flow rate,step pressure response of the valve control system,mean pressure and ripple amplitude,not only in the linear range,but also in the nonlinear range can be wel predicted; Good agreement between measured and calculated results was obtained,which proved that the model is helpful for designing a control strategy in a closed loop control system.

Simplified lateral free field boundary based on a lumped mass system

After reviewing the studies on the lateral artificial boundaries in dynamic soil-structure interactions,the free field boundary was theoretically analyzed in asymmetric-and symmetric-matrix forms.First,the lumped mass system was combined with viscous or viscoelastic elements to obtain a lumped mass-free field boundary.Second,typical examples were implemented using the finite element software ABAQUS.The incident shear wave was taken to be perpendicular to the bottom to verify the effectiveness of the lumped mass-free field under various sites:underground structures,uniform sites,and layered sites.Finally,the accuracy of the lumped mass-free field boundary was compared with those of the viscoelastic and roller boundaries on different calculation scales,soil damping ratios,structure sizes,and ground motion characteristics.Subsequently,the engineering design values for different damping ratios are given.The results show that the precision of the lumped mass-free field boundary was reasonable,and the operation was simple within the same engineering application.

LUMPED-PARAMETER MODEL OF MASS TRANSFER IN HEMODIALYZER WITH ULTRAFILTRATION

1 INTRODUCTIONHemodialysis with ultrafiltration,also called hemodiafiltration(HDF),is a main methodof treatment for patients with chronic renal failure.The HDF procedure providesadequate removals of both small and middle molecular weight toxic substamces fromuremic blood,which is not possible by dialysis or ultrafiltration alone.According toclinical experience[1],the HDF procedure is well accepied by the patients,and thetreatment time is reduced by using it.

Development of basic technique to improve seismic response accuracy of tributary area-based lumped-mass stick models

Although a detailed finite element(FE) model provides more precise results, a lumped-mass stick(LMS) model is preferred because of its simplicity and rapid computational time. However, the reliability of LMS models has been questioned especially for structures dominated by higher modes and seismic inputs. Normally, the natural frequencies and dynamic responses of a LMS model based on tributary area mass consideration are different from the results of the FE model. This study proposes a basic updating technique to overcome these discrepancies; the technique employs the identical modal response, D(t), to the detailed FE model. The parameter D(t) is a time variable function in the dynamic response composition and it depends on frequency and damping ratio for each mode, independent of the structure's mode shapes. The identical response D(t) for each mode is obtained from the frequency adaptive LMS model; the adaptive LMS model which can provide identical modal frequencies as the detailed FE model. Theoretical backgrounds and formulations of the updating technique are proposed. To validate the updating technique, two types of structures(a symmetric straight column and an unsymmetric T-shaped structure) are considered. From the seismic response results including base shear and base moment, the updating technique considerably improves the seismic response accuracy of the tributary area-based LMS model.

Lumped Mass Finite Element Method of the Nonlinear BBM Equation

In this paper, the full-discrete approximation scheme of the lumped mass nonconforming finite element method for BBM equation is discussed. Without the Riesz projection used in the traditional finite element analysis, the optimal error estimations are derived based on interpolation technique and special properties of element.

埃尔米特梁单元的分块对角与高阶质量矩阵

埃尔米特梁单元常用的集中质量矩阵,是由挠度自由度对应的一致质量矩阵元素通过行求和或节点积分构造.然而,数值结果表明该集中质量矩阵在求解包含自由端的梁振动问题时,会出现频率精度掉阶现象.本文首先从保障质量矩阵最优收敛性的数值积分精度出发,分别针对三次和五次梁单元,发展了质量矩阵的梯度增强节点积分方案.利用梯度增强节点积分方案,可以得到具有分块对角形式的单元质量矩阵,而其组装的整体质量矩阵除边界节点外仍然呈现对角形式.对于两种单元,其分块对角质量矩阵分别具有4阶最优精度和6阶次优精度.再者,将标准一致质量矩阵和具有同阶精度的梯度增强节点积分质量矩阵进行优化组合,建立了具有超收敛特性的高阶质量矩阵.最后,通过数值算例系统验证了三次和五次单元的分块对角与高阶质量矩阵的频率计算精度.

拖曳系统中瑞利阻尼系数变化在回转过程中对拖缆动力学振动响应的影响

海洋拖曳系统是典型的刚柔多体系统。需要指出的是,到目前为止,绝大多数的关于海洋拖曳缆体系统的动力学问题研究都没有非常充分地考虑到阻尼的作用。但在海洋拖曳系统的结构动力学分析中,特别是拖缆回转过程中的动态响应分析中,阻尼的作用是不可忽略的。且由于阻尼的存在,拖缆的模态特性也会呈现出高度的复杂性。为探究瑞利阻尼在拖缆回转过程中的影响,基于凝集质量法对瑞利阻尼的在拖缆系统中的表达形式进行了进一步的整理与分解,并对各个阻尼分量的影响进行了归纳总结,得到了一些较为通用性的结论,对于实际海上拖曳作业有一定的指导意义。

多脉冲加载下PBX装药的应力放大效应

针对弹体侵彻过程中装药常常受到多脉冲载荷作用的问题,提出了一种装药多脉冲加载装置,研究了多脉冲加载下装药的应力放大效应。基于集中质量法建立了多脉冲加载装置的等效弹簧模型,对产生应力放大的条件进行了探讨。结果表明,多脉冲载荷频率与装药固有频率匹配时系统发生共振,装药产生响应放大,放大倍数随结构间隙宽度的增加而降低。装药多脉冲加载下存在一个时间区间,撞击加载的发生时刻落在该区间内时系统可产生放大效果。对高聚物黏结炸药(polymer bonded explosive,PBX)模拟材料,实现了实验室条件下应力幅值百兆帕、脉冲间隔毫秒级、脉冲次数3次且幅值逐渐放大的多脉冲载荷加载。

水下拖曳系统拖缆末端不确定性量化分析

在多变的海洋环境中,水下拖曳系统拖缆优化设计与拖体精确控制的关键在于拖缆末端不确定性的量化。针对传统不确定性量化方法蒙特卡罗(MC)法计算成本高、精度低的问题,提出一种基于多项式混沌(PC)的拖缆末端不确定性量化方法。利用拉丁超立方采样获取拖缆参数的样本集,并代入集中质量法模型求得拖缆末端位置坐标。通过PC方法生成拖缆末端响应的代理模型,根据正交多项式的特点量化拖缆末端的不确定性,同时与MC方法进行对比。结果表明:相比于MC方法,PC方法的计算结果关于样本数量的收敛速度更快,精度更高;运动响应不确定性与拖缆轴向长度近似正比例关系;缆长增大将导致末端的不确定性增大,且增大趋势逐渐平缓;拖缆参数不确定性一定时,增大母船航速有助于提高拖体在高度上的稳定性。PC方法的准确性和高效性得到验证。同时,拖缆末端不确定性量化分析结果可为相关工程问题提供指导。

考虑柱体摇摆效应的殿堂式木结构古建筑非线性地震反应分析

为了准确描述半刚性榫卯连接柱架在地震作用下的动力性能,采用非线性转动弹簧以模拟柱体在地震作用下的摇摆行为,基于柱体、榫卯节点及斗栱的非线性恢复力模型,提出了单层殿堂式木结构地震分析的集中质量简化分析模型,进行了地震作用下的结构动力响应时程分析。通过计算时程曲线与振动台试验结果的对比分析发现,未考虑柱体摇摆的计算值与试验值的误差较大,考虑摇摆效应的整体结构时程曲线计算峰值与柱架的实际位移峰值误差相对较小,且峰值出现的时间基本相同。基于简化模型进一步进行了参数分析,结果表明:竖向荷载可以显著降低殿堂式木结构的地震位移响应;柱高越大,结构的地震位移响应越大;结构的地震位移响应随着榫卯节点转动刚度的增大而显著降低;斗栱数量的增加提高了整体结构的抗侧刚度,从而降低了结构的地震位移响应。研究结果可为木结构古建筑在地震作用下的性能评估提供计算依据。

固-液两相内流激励下悬臂输流管道稳定性特征研究

对输送介质为固-液两相流的悬臂输流管道模型进行了数值研究.首先,采用能量法以及哈密顿变分原理建立了固-液两相内流激励下悬臂输流管道的动力学方程.随后,用Galerkin方法对方程进行离散,将偏微分方程转化为一系列常微分方程构成的方程组.最后,利用特征值法以及Newton-Raphson迭代法对管道的稳定性特征展开了数值求解.对4种不同无量纲端部质量块下无量纲细长比、无量纲重力系数、以及无量纲固相比这几个重要参数对临界速度的影响展开了研究.研究结果表明,当内流速度小于临界速度时,系统特征频率虚部均为正数,结构振动形式表现为衰减振动;当内流速度超过临界速度时,系统的某阶特征频率虚部会出现负数,结构振动形式表现为颤振失稳.此外,端部质量对临界速度的影响随着重力系数的增加呈下降趋势;当重力系数增加到一定值时,临界速度值基本不受端部质量影响.当细长比和固相比较小时,随着端部集中质量块质量的增加,临界速度均呈下降趋势;当细长比和固相比较大时,临界速度不再呈单调变化趋势,而是呈现出较为复杂的变化趋势.该研究对悬臂输流管道早期的合理设计,以及服役期的安全工作均有着重要的理论和工程价值.

地下水位对核电结构地震反应的影响分析

核电结构大多沿海或沿江、河而建,在地下水位以下,土体孔隙中的流体对土层的地震响应有较大影响,进而影响核电结构的响应。本文采用饱和多孔介质模型,考虑土-结相互作用效应,分析地下水位对核电结构地震反应的影响。通过传递矩阵方法,得到干土-饱和土水平成层场地的自由场,并结合透射人工边界,实现土-结相互作用分析的波动输入;采用土-结相互作用的分区并行计算方法,实现饱和土和结构相互作用分析。其中,含地下水位的场地土体采用广义饱和多孔介质模型描述,通过自编FORTRAN程序用集中质量显式有限元结合透射人工边界进行模拟,结构通过ANSYS中的隐式有限元进行分析。以某一核电结构为例,分析了0,−10,−20,−30,−40 m不同地下水位的五种场地上,土-基础-核电结构体系的动力响应。结果表明,地下水位对基础和结构的位移影响不大,对加速度的影响较大。

带式输送机转载点振动冲击分析及转载溜槽结构优化

在煤炭生产系统中,带式输送机转载溜槽的合理设计可提高煤炭企业经济效益,因而转载点物料流的冲击分析以及转载溜槽的结构优化对煤炭企业生产运输具有重要意义。以某露天煤矿带式输送机转载系统为研究对象,针对转载系统存在的块煤破碎质量比过高、对下方带式输送机振动冲击过大以及转载时衬板磨损严重等问题,进行转载点的物料流特性实验分析以及溜槽结构的优化设计。

纯流下网目形状对圆柱形网衣变形的影响

网衣容积对鱼类养殖至关重要,研究网目形状对网衣变形的影响可以更好地提高网衣的性能.采用集中质量模型并建立柔性网衣运动控制方程,通过前人试验验证了数值模型的准确性.以某圆柱形网衣为例,针对不同网目形状,在不同流速下,对网衣进行了数值模拟,研究网目形状对网衣变形的影响.结果表明:正方形网目网衣底端前点的水平位移大于后点的水平位移,前点的垂直位移则小于后点的垂直位移,正六边形网目网衣则相反;在0.3 m/s流速下,正六边形网目网衣的容积剩余系数比正方形网目网衣多8.4%;正六边形网目比正方形网目网衣容积损失更低,网衣变形得到一定改善.

驱动桥准双曲面齿轮传动系统振动特性分析

驱动桥是微车传动系统的核心部件之一,承受复杂的载荷,影响整车的安全、舒适和动力,其振动和噪声对整车舒适性(NVH)性能有重要影响。为掌握驱动桥振动响应的影响规律,实现驱动桥动态特性的主动控制,本文以驱动桥准双曲面齿轮传动系统为研究对象,考虑主从齿时变啮合刚度、阻尼、传动误差和冲击等激励,基于集中质量法构建驱动桥齿轮传动系统的多变参数耦合振动模型,并依据牛顿第二定律推导其振动微分方程组,采用RK算法求解方程组;对比准双曲面齿轮修形优化前后主、从动齿轮的垂直、扭转和轴向振动数值解,并讨论输入转速和加载扭矩的改变对系统振动特性的影响规律。结果表明:优化后的齿轮运转振动值减小;主从齿的垂直和轴向振动规律复杂,处于近似混沌运动状态;扭转方向上呈现拟周期运动;输入转速和加载扭矩的改变对主从齿轴向振动影响最大,垂直方向次之,扭转方向最小。进一步对驱动桥总成进行振动测试分析,结果表明,新状态样件的动态性能更优,测试数据的趋势与理论分析结果符合较好。该研究成果可应用于分析驱动桥的关键激励因素,预测振动响应,提升产品的动态性能。