水下悬跨输流管道动力稳定性的DQ解法

考虑水下粘弹性输流管道在管外流体附加阻尼、管内管外流体流动、管道轴向力、管内压强和流体质量比等因素的影响,尝试运用微分求积法对其涡激振动和流致振动的动力稳定性进行分析研究,通过算例分析说明DQ法用于水下管道悬空段的动力稳定性分析、疲劳分析、可靠性分析及设计是可行的,该方法具有原理简单、计算量少、易于编程实现、精度令人满意等特点,本文结论对于工程计算理论及工程应用具有参考价值.     

线性变厚度粘弹性矩形板在随从力作用下的动力稳定性

利用粘弹性微分型本构关系和薄板理论,对线性变厚度粘弹性矩形薄板建立了在切向均布随从力作用下的运动微分方程,采用微分求积法研究了在随从力作用下线性变厚度粘弹性矩形薄板的稳定性问题,具体对对边简支对边固支和三边简支一边固支条件下体变为弹性、畸变服从Kelvin-Voigt模型的变厚度粘弹性矩形板在随从力下的广义特征值问题进行了求解,分析了薄板的长宽比、厚度比及材料的无量纲延滞时间的变化对随从力作用下矩形薄板的失稳形式及相应的临界荷载的影响.     

谐激励作用下输流曲管的混沌振动研究

研究了谐激励作用下输流曲管在系统参数区域内的混沌振动．基于牛顿法导出了输流曲管模型的非线性控制方程,并利用微分求积法对此方程在空间域进行离散,导出了输流曲管的非线性动力学方程组．在此基础上,对输流管道的动力响应进行了数值模拟．采用分岔、相平面、时间历程和庞加莱映射图等手段分析发现,在流速和激励频率的参数区域内,系统将可能发生包括混沌振动在内的多种运动形式．系统可经由倍周期分岔或概周期运动通向混沌．分析结果为工程输流管道模型的合理设计提供了参考．     

三参量固体模型粘弹性输流管道的动力特性分析

推导了三参量固体模型粘弹性输流管道的振动微分方程 ,计算了在不同无量纲松弛系数和弹性常数比下管道的无量纲临界流速和无量纲自振复频率 ,并给出了前三阶复频率与流速的关系 .计算结果表明 ,质量比、无量纲松弛系数及无量纲弹性常数比对输流管道的动力特性均有影响 .     

微分求积法的特性及其改进

微分求积法已在科学和工程计算中得到了广泛应用。然而,有关时域微分求积法的数值稳定性、计算精度即阶数等基本特性,仍缺乏系统性的分析结论。依据微分求积法的基本原理,推导证明了微分求积法的权系数矩阵满足V-变换这一重要特性;利用微分求积法和隐式Runge-Kutta法的等值性,证明了时域微分求积法是A-稳定、s级s阶的数值方法。在此基础上,为进一步提高传统微分求积法的计算精度,利用待定系数法和Padé逼近,推导出了一类新的s级2s阶的微分求积法。数值计算对比结果验证了所提出的新微分求积法比传统的微分求积法具有更高的计算精度。     

集中载荷作用下梯度复合材料梁的小波-微分求积法分析

将梯度复合材料梁作为平面应力问题处理,采用小波和微分求积混合法,对集中荷载作用下结构的响应进行了分析.考虑材料特性参数沿高度方向呈梯度分布,在该方向上采用广义微分求积法进行离散;鉴于广义微分求积法求解集中荷载问题精度不高的缺点,在梁的长度方向上引入对突变信号敏感的小波插值函数.数值计算表明,小波-微分求积混合法不仅保留了广义微分求积法高效的优点,而且能够很好地模拟结构局部化特征.     

混合微分求积法在功能梯度材料平板柱形弯曲问题中的应用

利用混合微分求积法,对任意荷载作用下不同材料梯度分布的功能梯度材料平板柱形弯曲问题进行了分析。针对广义微分求积法求解集中荷载问题精度不高的缺点,本文利用小波微分求积法进行了改进。由于小波对突变信号具有良好的自适应描述能力,因此在平板宽度方向上,利用小波微分求积法可以有效地处理集中荷载;而在材料梯度变化的板厚方向上,则利用广义微分求积法计算量小且精度高的特点进行离散计算。计算表明,混合微分求积法不仅保留了广义微分求积法高效的特点,而且能有效地求解任意荷载作用的问题。通过算例,分析了在机械荷载作用下,材料不同梯度形式、平板上下表面材料性质差异对功能梯度平板结构响应的影响。     

三参量固体模型粘弹性输液管道的动力特性分析

推导了三参量固体模型粘弹性输流管道的振动微分方程，计算了在不同无量纲松弛系数和弹性常数比下管道的无量纲临界流速和无量纲自振复频率，并给出了前三阶复频率与流速的关系。计算结果表明，质量比，无量纲松弛系数及无量纲弹性常数比对输流管道的动力特性均有影响。     

粘弹性地基上粘弹性输流管道的稳定性分析

从Winkler假设和单轴线性粘弹性本构方程出发,推导了Kelvin-Voigt粘弹性地基上三参量固体模型输流管道的运动微分方程,采用改进的有限差分法,分析了管道和地基的粘弹性参数对输流管道无量纲复频率和无量纲流速之间的变化关系的影响。     

梁式结构受移动荷载作用非平稳随机振动的DQ-PEM方法

针对梁式结构受移动荷载作用的非平稳随机振动问题,提出了一种综合利用微分求积法和虚拟激励法DQ-PEM的新方法。梁式结构受移动荷载作用的振动控制方程为含Dirac函数的偏微分方程,利用微分求积(DQ)-积分求积法(IQ)法将其振动控制方程转化为不含Dirac函数的常微分方程。同时,将表示荷载位置变化的Dirac函数视为移动荷载的非平稳化函数,再结合虚拟激励法的思想,可得梁式结构在确定性荷载作用下的虚拟响应,进而得到其非平稳随机响应。通过工程算例验证了该方法的准确性与有效性,并进一步讨论了不同速度和不同边界条件下梁式结构受移动荷载作用的随机振动问题。     

Vibration and stability of an axially moving beam immersed in fluid

Vibration and stability are investigated for an axially moving beam in fluid and constrained by simple supports with torsion springs. The equations of motion of the beam with uniform circular cross-section, moving axially in a horizontal plane at a known rate while immersed in an incompressible fluid are derived first. An “axial added mass coefficient” and an initial tension are implemented in these equations. Based on the Differential Quadrature Method (DQM), a solution for natural frequency is obtained and numerical results are presented. The effects of axially moving speed, axial added mass coefficient, and several other system parameters on the dynamics and instability of the beam are discussed. Particularly, natural frequency in terms of the moving speed is presented for fixed–fixed, hinged–hinged and hybrid supports with torsion spring. It is shown that when the moving speed exceeds a certain value, the beam becomes subject to buckling-type instability. The variations of the lowest critical moving speed with several key parameters are also investigated.     

输液管振动与稳定性研究的新进展——从宏观尺度到微纳米尺度

本文围绕不同尺度级的输液管结构,针对液流引起的管道振动与稳定性综述了目前已有的几种物理和数学模型,详细介绍了梁模型输液管的各类振动控制方程,重点讨论了宏观尺度、微米尺度和纳米尺度下输液管振动方程的异同点。在此基础之上,进一步概述了近几年这些输液管振动与稳定性问题研究的现状和一些重要研究结果,其中也包括作者们近期的相关工作。最后对未来的研究趋势作了分析和预测。通过本文可以看到,输液管振动问题仍有不少难题尚未很好解决,特别是微纳米输液管的建模和流固耦振机理方面的研究亟需加强     

VIBRATION AND STABILITY ANALYSIS OF CANTILEVERED TWO-PIPE SYSTEMS CONVEYING DIFFERENT FLUIDS

This paper considers the dynamic stability of plane transverse oscillations of two cantilevered pipes interconnected along their outer radii and conveying different fluids with different flow speeds. Stability curves depicting the relation between the two flow speeds at the stability boundary are shown for a number of fluid-structure mass ratios. One fluid flow may dissipate energy delivered to the system by the other, if the speed of the first one is not too large. One pipe can thus be thought of as a stabilizer to the other, with the aim of increasing the critical speed of the primary flow. The stabilizing effect of one fluid on the other is clarified through considerations of an energy equation together with flutter oscillation shapes. The energy equation is also used to derive a relation between the two flow speeds and the phase speed of the flow-induced travelling bending wave.     

Thermal effect on vibration of non-homogenous visco-elastic rectangular plate of linearly varying thickness

An analysis for vibration of non-homogenous visco-elastic rectangular plate of linearly varying thickness subjected to thermal gradient has been discussed in the present investigation. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The governing differential equation of motion has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement at different points for the first two modes of vibration are calculated for various values of thermal gradients, non homogeneity constant, taper constant and aspect ratio for non-homogenous visco-elastic rectangular plate which is clamped on two parallel edges and simply supported on remaining two edges. Comparison studies have been carried out with homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.     

基于压缩蠕变试验的流变参数理论解析反演

大坝坝基的长期稳定性是大坝运营安全的重要保障, 而坝基岩体中的软弱夹层是影响其变形和稳定的重要因素. 为研究大岗山水电站坝基中辉绿岩脉软弱夹层在长期载荷作用下的变形机制, 在坝基边坡的试验平硐内垂直于软弱夹层进行了现场大型圆形刚性承压板压缩蠕变试验. 辨识得到可较准确表示其蠕变特性的5参量广义Kelvin模型, 克服了3 参量广义Kelvin模型收敛过快的缺陷. 基于弹性力学中的布辛涅斯克问题, 通过黏弹性理论中的拉普拉斯变换及逆变换, 推导出了刚性承压板下部岩体的5参量广义Kelvin模型表示的黏弹性变形公式, 并以此为基础反演得到流变参数.     

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

The Kelvin–Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin–Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts.These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.     

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.     

基于改进降维法的可靠度分析

单变量维数缩减法可以高效、准确地进行结构响应矩的分析.与传统的一阶可靠度算法FORM(First Order Reliability Method),二阶可靠度算法SORM(Second Order Reliability Method)相比,该方法不需要响应的导数,也不需要迭代搜索最可能失效点.然而近期的研究发现,该...     

Stability Analysis of Maxwell Viscoelastic Pipes Conveying Fluid with Both Ends Simply Supported

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