加权残数法用于侧向力作用下开有n排孔列的剪力墙的近似解

本文推导了侧向力作用下开有n排孔列的剪力墙的微分方程,选择了连梁剪应力r(x)的试函数,用加权残数法确定试函数中的待定常数,获得了描述真实的r(x)曲线的近似解析解.对剪力墙计算结果表明,加权残数法所得的结果与有限元法比较十分接近,但是加权残数法具有未知量少、误差估计方便,工作量减省、可得解析表达式等优点.     

积分方程的加权残数配点法

对于用积分方程式表示的物理问题,本文应用加权残数的配点法进行求解,使得求解方法简便、可靠、正确。与常规的求解微分方程的加权残数配点法相比较,本方法不需假定任何试函数。文中给出较多的算例,论证了本文提出的积分方程的加权残数配点法的有效性,可靠性和精确性。     

加权残数法解固体力学问题

加权残数法的概念大量的应用科学和工程问题往往归结为根据一定的边界条件和初值条件等来解所谓定解微分方程式.加权残数法 MWR(Method of Weighted Residuals)是一种数学方法,它可以直接从微分方程式中求得近似的解.其方法须先假设一个称为试函数的近似函数,引入微分方程式及边界条件,自然由于满足不了而出现了误差,称为残数.然后再选择一定的权函数与残数相乘要求它 ...     

基于无网格Galerkin法求解矩形绝缘管道内的磁流体流动

无量纲磁流体流动控制方程中的哈特曼数较大将导致数值计算发散或误差过大。将无网格Galerkin法引入绝缘管道内的稳定磁流体流动计算中,针对磁流体控制方程中大哈特曼数导致计算误差大的情况,对无网格Galerkin法添加了稳定项。计算结果表明,同等条件下,添加了稳定项的无网格Galerkin法总体相对误差远小于标准无网格Galerkin法的结果,且可以计算哈特曼数最大达50000绝缘管道内的磁流体流动。     

二维定常不可压缩粘性流动N-S方程的数值流形方法

将流形方法应用于定常不可压缩粘性流动N-S方程的直接数值求解,建立基于Galerkin加权余量法的N-S方程数值流形格式,有限覆盖系统采用混合覆盖形式,即速度分量取1阶和压力取0阶多项式覆盖函数,非线性流形方程组采用直接线性化交替迭代方法和Nowton-Raphson迭代方法进行求解.将混合覆盖的四节点矩形流形单元用于阶梯流和方腔驱动流动的数值算例,以较少单元获得的数值解与经典数值解十分吻合.数值实验证明,流形方法是求解定常不可压缩粘性流动N-S方程有效的高精度数值方法.     

加权残数法通用程序包MWRAP的开发技术与1程应用

要想使加权残数法广泛应用于工程实际问题,需要解决两方面的问题,一是精度问题,二是必须研制和开发通用软件。本文阐述了加权残数法通用程序包MWRAP的结构设计和功能设置及其前后处理技术,详细阐述了其前后处理程序的程序设计流程;在该软件中计算模块,所用的计算方法为加权残数和有限元耦合法,为此推导了加权残数和有限元耦合法的公式,从计算结果来看该方法具有较高的精度,可以满足工程需要。最后,运用MWRAP计算了钢管混凝土柱肩梁结构的位移和应力,与实验结果相比吻合较好,说明了MWRAP具有较高的精度,加上其完善的前后处理功能,可以应用于工程实际问题。     

横向荷载作用下弹性地基上梁的主共振分析

基于Winkler地基模型及Euler-Bernoulli梁理论,建立了弹性地基上有限长梁的非线性运动方程.运用Galerkin方法对运动方程进行一阶模态截断,并利用多尺度法求得该系统主共振的一阶近似解.分析了长细比、地基刚度、外激励幅值和阻尼系数等参数对系统主共振幅频响应的影响,然后通过与非共振硬激励情况对比分析主共振对其动力响应的影响.结果表明:主共振幅频响应存在跳跃和滞后现象;阻尼对主共振响应有抑制作用;主共振显著增大系统稳态动力响应位移.     

圆柱形扁壳弹塑性分析

本文采用加权残数法中的离散型最小二乘法求圆柱形扁壳的弹塑性解,文中的方法可以用于较为复杂载荷和边界条件的圆柱形扁壳的弹塑性问题。 采用加权残数法有它独特的优点:简便、准确、迅速、工少价廉,而且非常适宜于应用微型计算机来实施。     

功能梯度圆锥扁壳的1:2内共振研究

对热载荷和机械载荷共同作用下的功能梯度圆锥扁壳进行了1:2内共振分析。假设材料属性与温度有关,材料组分沿厚度方向呈幂律梯度变化,基于一阶剪切变形理论和von-Karman几何非线性关系,运用Hamilton原理建立功能梯度圆锥扁壳的非线性动力学方程;采用Galerkin法将运动控制方程离散成一个两自由度非线性动力学系统,采用多尺度法对上述方程进行摄动分析,获得了系统的平均方程,进一步得到频率响应函数和力幅响应函数。研究了材料体积分数指数和面内载荷对幅-频响应特性的影响,结果表明:研究可以得出:改变材料体积分数指数会影响材料中金属的含量及分布,从而引起幅-频响应曲线刚度特性和共振峰带宽的变化;面内载荷的变化不会影响幅-频响应曲线的刚度特性,但是会改变共振峰的带宽。本文还研究了振幅跳跃现象,通过Runge-Kutta法对共振系统进行数值仿真,研究了面内载荷对系统非线性动力学行为的影响,得出:随着面内载荷的变化,系统的运动从周期运动经历概周期运动变成混沌运动。     

含集中质量矩形薄板的动力学建模与质量调幅分析

基于经典薄板理论和von Kármán非线性理论,采用Hamilton原理,首先建立了含集中质量矩形薄板的动力学方程,并结合Galerkin法进行模态截断,获得双模态非线性动力学控制方程组;随后,运用多尺度法,引入频率失调参数,重点研究了主共振与1∶3内共振联合作用下系统的非线性动力学特性,获得了幅-频特性表达形式。根据振动同步性以及幅-频曲线的极值特性,在分析参数范围内,发现当集中质量为0.06kg时,第一阶幅频曲线非线性现象衰减,且第二阶幅频曲线取到最小值。最后实例以集中质量作为调谐参数,分析了质量变化对振幅的影响,计算结果表明,质量在某一范围内对主共振与1∶3内共振联合下的第一阶模态振幅影响较小,但对第二阶模态振幅有较强的调制作用。     

分析弹性支承输流管道的失稳临界流速

研究了两端弹性支承输流管道静态失稳和动态失稳临界流速. 根据梁模型横向弯曲振动模态 函数，由两端弹性支承的边界条件得到了其模态函数的一般表达式. 根据特征方程具体分析 了弹性支承刚度、质量比、流体压力和管截面轴向力等主要参数对失稳临界流速的影响. 数 值计算结果表明，管道在弹性支承下的动力稳定性比较复杂，在较小的弹性支承刚度和较小 的参数范围内，管道主要表现为动态颤振失稳；在较大的弹性支承刚度和较大的参数作用下， 管道的失稳形式主要表现为静态失稳；并且失稳临界流速随流体压力和管截面轴向压力的增 加而下降，随管截面轴向拉力的增加而上升.     

DYNAMIC STABILITY OF A BEAM-MODEL VISCOELASTIC PIPE FOR CONVEYING PULSATIVE FLUID

The dynamic stability in transverse vibration of a viscoelastic pipe for conveying pulsative fluid is investigated for the simply-supported case.The material property of the beam- model pipe is described by the Kelvin-type viscoelastic constitutive relation.The axial fluid speed is characterized as simple harmonic variation about a constant mean speed.The method of mul- tiple scales is applied directly to the governing partial differential equation without discretization when the viscoelastic damping and the periodical excitation are considered small.The stability conditions are presented in the case of subharmonic and combination resonance.Numerical results show the effect of viscosity and mass ratio on instability regions.     

A parametric study on nonlinear flow-induced dynamics of a fluid-conveying cantilevered pipe in post-flutter region from macro to micro scale

A mathematical formulation is proposed to investigate the nonlinear flow-induced dynamic characteristics of a cantilevered pipe conveying fluid from macro to micro scale. The model is developed by using the extended Hamilton's principle in conjunction with the inextensibility condition and laminar and turbulent flow profiles as well as modified couple stress theory. The current model is capable of recovering the classical model of cantilevered pipe conveying fluid by neglecting the couple stress effect. The governing equation of motion is presented in dimensionless form in a convenient and usable manner. To solve the problem at hand, the integro-partial-differential equation of motion is discretized into a set of ordinary differential equations via Galerkin method. Afterward, a Runge–Kutta's finite difference scheme is employed to evaluate the nonlinear dynamic response of the cantilevered pipe conveying fluid. A parametric study is carried out to examine the influences of mass parameter and dimensionless mean flow velocity on the nonlinear dynamic characteristics of the cantilevered pipe conveying fluid in post-flutter region. The role of size-dependency in the nonlinear behavior of pipe is explored by converting the new set of dimensionless parameters into the conventional one. Eventually, some convergence studies are performed to indicate the reliability of present results.     

具有弹性支承的圆管在内外部流激发下动力特性及实验研究

本文建立了具有弹性支承的圆管在内外部流激发下的力学模型.推导了内部流与静止外部流作用下圆管的耦联振动方程.提出了确定弹性系数的方法.采用振型叠加法分析圆管动力特性问题.对内部流与静止外部流情况下圆管固有频率进行了计算和测量,计算值与实验值吻合较好.另外,对内外流同时激发下圆管的固有频率进行了测量,得到若干对工程实际有用的结论.     

Stability analysis of viscoelastic curved pipes conveying fluid

Based on the Hamilton' s principle for elastic systems of changing mass, a differential equation of motion for viscoelastic curved pipes conveying fluid was derived using variational method, and the complex characteristic equation for the viscoelastic circular pipe conveying fluid was obtained by normalized power series method. The effects of dimensionless delay time on the variation relationship between dimensionless complex frequency of the clamped-clamped viscoelastic circular pipe conveying fluid with the Kelvin-Voigt model and dimensionless flow velocity were analyzed. For greater dimensionless delay time, the behavior of the viscoelastic pipe is that the first, second and third mode does not couple, while the pipe behaves divergent instability in the first and second order mode, then single-mode flutter takes place in the first order mode.     

Nonlinear dynamics of a pipe conveying pulsating fluid with parametric and internal resonances

In this paper, the nonlinear planar vibration of a pipe conveying pulsatile fluid subjected to principal parametric resonance in the presence of internal resonance is investigated. The pipe is hinged to two immovable supports at both ends and conveys fluid at a velocity with a harmonically varying component over a constant mean velocity. The geometric cubic nonlinearity in the equation of motion is due to stretching effect of the pipe. The natural frequency of the second mode is approximately three times the natural frequency of the first mode for a range of mean flow velocity, resulting in a three-to-one internal resonance. The analysis is done using the method of multiple scales (MMS) by directly attacking the governing nonlinear integral-partial-differential equations and the associated boundary conditions. The resulting set of first-order ordinary differential equations governing the modulation of amplitude and phase is analyzed numerically for principal parametric resonance of first mode. Stability, bifurcation, and response behavior of the pipe are investigated. The results show new zones of instability due to the presence of internal resonance. A wide array of dynamical behavior is observed, illustrating the influence of internal resonance.     

FORCED VIBRATIONS WITH INTERNAL RESONANCE OF A PIPE CONVEYING FLUID UNDER EXTERNAL PERIODIC EXCITATION

Applying the multidimensional Lindstedt-Poincaré (MDLP) method, we study the forced vibrations with internal resonance of a clamped-clamped pipe conveying fluid under external periodic excitation. The frequency-amplitude response curves of the first-mode resonance with internal resonance are obtained and its characteristics are discussed; moreover, the motions of the first two modes are also analyzed in detail. The present results reveal rich and complex dynamic behaviors caused by internal resonance and that some of the internal resonances are decided by the excitation amplitude. The MDLP method is also proved to be a simple and efficient technique to deal with nonlinear dynamics.     

含非线性能量汇的简支输液管非线性振动控制研究

论文建立了一个含有非线性能量汇(NES)装置并输运脉动内流的简支输液管道理论模型, 研究了NES装置对管道的非线性动力学特性与振动控制的影响. 利用Galerkin和龙格库塔法, 得到了在含NES和不含NES装置时管道动力学响应的数值结果. 研究表明, NES装置能有效地抑制管道振动. 通过对比可知, NES对管道系统的稳定性和非线性振动控制有着明显的影响. 此外, 本文还详细讨论了NES装置相关参数对系统的动力学影响. 结果表明, 增大NES的弹簧刚度、阻尼和质量比有利于管道减振, 且最佳安装位置在管道中点. 此外, 增大阻尼?能缩小失稳激励频率区域, 而其他参数的变化对失稳激励频率区域影响较小.     

输液曲管平面内振动的波动方法研究

采用Flügge曲梁模拟弯曲管道,推导了管内流体的加速度,在总体轴线不可伸长假定的基础上建立了曲管平面内振动的动力学方程;采用波动方法,获得了曲管内振动波的传播和反射矩阵,提出了计算曲管平面内振动固有频率的数值方法。算例分析中,通过计算两端固定半圆形曲管的临界流速并与已有文献结果对比,验证了本文方法的正确性。最后,计算了两端固定半圆形曲管在四种不同流速下的前四阶固有频率,结果表明,管内流速的增大会降低管道的固有频率,当流速增大到某一特定值时,管道的一阶固有频率消失。     

THE DYNAMIC BEHAVIORS OF VISCOELASTIC PIPE CONVEYING FLUID WITH THE KELVIN MODEL

Based on the differential constitutive relationship of linear viscoelastic, material, a solid-liquid coupling vibration equation for viscoelastic pipe conveying fluid is derived by the D'Alembert's principle. The critical flow velocities and natural frequencies of the cantilever pipe conveying fluid with the Kelvin model (flutter instability) are calculated with the modified finite difference method in the form of the recurrence formula. The curves between the complex frequencies of the first, second and third mode and flow velocity of the pipe are plotted. On the basis of the numerical, calculation results, the dynamic behaviors and stability of the pipe are discussed. It should be pointed out that the delay time of viscoelastic material with the Kelvin model has a remarkable effect on the dynamic characteristics and stability behaviors of the cantilevered pipe conveying fluid, which is a gyroscopic non-conservative system.