海洋立管双模态动力学分岔分析

为研究剪切流作用下顶张力立管的涡激振动响应规律,将立管简化为Euler-Bernoulli梁模型,用van der Pol尾流振子描述流体的作用,建立了立管涡激振动的非线性动力学模型.基于二阶Galerkin模态离散所得常微分方程组,采用谐波平衡法、Poincaré映射方法和Lyapunov指数法分析系统响应特点.研究结果表明:随着流速的增加,系统响应在周期运动和概周期运动间多次转换,其中周期解区域对应系统的涡激共振区;谐波平衡法结果能够较准确地预测涡激共振区周期解的振幅和频率,以及非涡激共振区概周期解的主要频率成分.     

海洋立管涡激损伤分析的虚拟激励法概述

立管是连接海底钻井和海上平台的重要系统.涡激振动是造成立管疲劳损伤的主要因素.受海流的随机作用,立管涡激振动表现出不确定性,对这种随机振动进行快速有效地分析,对于立管的工程设计具有非常重要的意义.考虑随机激励作用,要比确定性激励困难得多,虚拟激励法对于克服这种困难具有很好的效果.近年来,应用虚拟激励法分析立管的涡激损伤问题,取得一些成果,该文对此作一概略的叙述.     

用子波谱分析壁湍流多尺度结构的能量传递

测量了壁湍流不同法向位置的流向速度.用子波变换研究湍流能谱,表明子波全局谱是Fourier谱按子波尺度加权平均的结果,高阶消失矩的子波变换能够表征湍谱的衰减特性;子波局部谱显示边界层内涡的变形、破碎等现象与边界层法向位置有关,含能涡结构呈多尺度分布,随着测点远离壁面,含能涡的尺度增大;在缓冲区出现更高频的小尺度含能涡,在外区能量集中在低频大尺度涡结构中,含能涡的频带变窄.     

部分埋入水中椭圆柱体弯曲自由振动

本文研究了部分埋入水中椭圆柱体弯曲自由振动.首次给出柱水耦联体系振型函数的精确解和以有限阶行列式表示的频率方程.指出水的效应等价于一个附加的分布质量,因此,水中柱体的振动频率低于无水时柱体的振动频率.     

方柱/板结合部马蹄涡流动结构的动力学模态分解

方柱/板结合部区域的马蹄涡系统存在多频流动现象.为了研究各频率所对应的振荡规律及其潜在的动力学信息,对方柱/板结合部处于周期振荡流动状态的马蹄涡系流动结构进行数值模拟,发现处于周期振荡流动状态的马蹄涡系为倍频流动现象.运用动力学模态分解(DMD)技术对方柱体上游对称面上的速度场进行模态分解,将所得到的第1、2、3阶模态分别叠加到平均流模态进行模态重构并在时域上进行推进演化分析.结果表明:周期振荡马蹄涡系以不同尺度马蹄涡间的相互卷并为主,发现了马蹄涡间不同的卷并方式.     

不可压缩Navier-Stokes方程数值模拟

建立不可压缩Navier-Stokes方程的Crank-Nicolson有限差分方法,数值模拟了在初始正弦波下的二维水槽内流体受到倾斜激励时流场和涡的演变机制.数值结果表明,初始波为正弦波时,流场内出现一个单涡,单涡下沉变成了两个小涡,两个小涡消失后流场内部出现三条规则的流场带,最后这三条流场带演变成一个尖涡,尖涡在周围流体的作用下演变成一个单涡,最后单涡在自由面消失,当耗散系数和Reynolds数增大时,流场和涡演化的周期变小.     

隔水套管波流联合作用下非线性动力响应

考虑流及波流联合作用,研究了深水套管的涡激非线性振动．将套管简化为梁模型,计及Morison非线性流体动力和涡激荷载,建立套管的涡激振动方程．采用Korolov函数求解套管的固有频率和模态,提出了计算涡激非线性动力响应的Galerkin方法,计算了160 m水深中170 m长套管的固有频率和模态,研究了流引起的主共振和波流联合引起的组合共振．计算结果表明波流联合作用下套管的动力响应明显增大,结果也揭示了波流联合激励下套管复杂的动力响应特性．     

直管束流固耦合振动的数值模拟

为了研究反应堆结构中的诸如燃料棒、蒸汽发生器和其它换热器传热管束等的流体-结构交互作用问题,利用有限体积法离散大涡模拟(large eddy simulation, LES)的流体控制方程,用有限元方法求解结构动力学方程,并结合动网格技术,建立三维流体诱发振动的数值模型,模拟直管束中流体的流动及结构振动,实现计算结构动力学(computational structure dynamics, CSD)与计算流体力学(computational fluid dynamics, CFD)之间的联合仿真．首先,基于流固耦合方法对单管的流致振动特性进行了详细分析,得到了其动力学响应与流场特性;其次基于建立的传热管束流致振动计算模型,研究了两并列管、两串列管以及3×3正方形排列管束的流致振动行为．     

Experimental Study on the Vortex-Induced Vibration of Fixed-Hinged Flexible Risers北大核心CSCD

海洋立管顶部常铰接于浮式平台下方,在海流激励下存在涡激振动响应,潜在疲劳失效的风险.该文采用非介入光学测试方法（高速摄像）,对布置于循环水槽中顶部铰接-底部固定的悬链线柔性立管进行了振动响应研究.实验结果表明,立管三个方向被激发的振动模态阶数与主导振动频率均随约化速度的增加而逐渐升高,平面外的最大均方根振幅在模态过渡时有先降后升的变化,与振动模态分支相呼应.流体与立管之间能量传递在不同方向的分布存在一定差异,导致不同步的模态过渡现象.平面内振动存在与平面外振动主导频率吻合的频率,根据其是否主导对应管段的平面内振动,将其分为强耦合和弱耦合两种模式.     

变截面二维功能梯度微梁的振动和屈曲特性北大核心CSCD

基于修正的偶应力理论和Timoshenko梁理论,应用变分原理建立了变截面二维功能梯度微梁的自由振动和屈曲力学模型.模型中包含金属组分和陶瓷组分的材料内禀特征尺度参数,可以预测微梁力学行为的尺度效应.采用Ritz法给出了任意边界条件下微梁振动频率和临界屈曲载荷的数值解.数值算例表明:微梁厚度减小时,无量纲一阶频率和无量纲临界屈曲载荷增大,尺度效应增强.锥度比对微梁一阶频率的影响与边界条件密切相关,同时,对应厚度和对应宽度锥度比的影响也有明显差异.变截面微尺度梁无量纲一阶频率随着陶瓷和金属的材料内禀特征尺度参数比的增加而增大,且不同边界条件时增大程度不同.厚度方向和轴向功能梯度指数对微梁的一阶频率和屈曲载荷也有显著的影响.     

Reduced-order model for laminar vortex-induced vibration of a rigid circular cylinder with an internal nonlinear absorber

The nonlinear interaction of a laminar flow and a sprung rigid circular cylinder results in vortex-induced vibration (VIV) of the cylinder. Passive suppression of the VIV by attaching an internal nonlinear vibration absorber that acts, in essence, as a nonlinear energy sink (NES) to the cylinder has been observed in finite-element computations involving thousands of degrees of freedom (DOF). A single-DOF self-excited oscillator is developed to approximate the limit-cycle oscillation (LCO) of the cylinder undergoing VIV. This self-excited oscillator models the interaction of the flow and the cylinder. Then, a two-DOF reduced-order model for the system with the internal NES is constructed by coupling the single-DOF NES to the single-DOF self-excited oscillator. Hence, the complicated high-dimensional system of flow-cylinder-NES involving thousands of DOF is reduced to a two-DOF model. The two targeted energy transfer mechanisms responsible for passive VIV suppression that are observed in the finite-element computations are fully reproduced using the two-DOF reduced-order model. This reduction of the dynamics to an easily tractable low-dimensional reduced-order model facilitates the approximate analysis of the underlying dynamics. Moreover, the underlying assumptions of the order reduction, and the parameter ranges of validity of the reduced-order model are formulated and systematically studied.     

Numerical evaluation of the suppression effect of a free-to-rotate triangular fairing on the vortex-induced vibration of a circular cylinder

The suppression of vortex-induced vibration (VIV) of a circular cylinder with a free-to-rotate triangular fairing in the Reynolds number range of Re = 1100–6100 is numerically investigated using computational fluid dynamics. The unsteady Reynolds-averaged Navier–Stokes equations and the shear stress transport k–ω turbulence model coupled with an improved fourth-order Runge–Kutta method are used to solve the wake flow, the structure's vibration, and the fairing's rotation. The computational model is validated with the available experimental results for a cylinder with an attached short-tail fairing. The numerical results indicate that the triangular fairing has a positive role in suppressing vibration when it achieves a stable position deflected from the flow direction. The suppression effect is sensitive to the incoming flow velocity. The fairing shifts from a stable state to an unstable one when the flow velocity varies. Therefore, maintaining the hydrodynamic stability of the fairing is the key to achieving success in vibration suppression, and the stability is dependent on the characteristic length and the rotational friction. Although the strong flapping of the 70° triangular fairing excites a more vigorous vibration, it may be used as an amplifier of VIV for energy harvesting.     

Vibrational mixing of a fluid between two quasiconcentric cylinders

We consider the possibility of intense mixing of a viscous fluid in the gap between two quasiconcentric cylinders, with one of the cylinders performing high-frequency vibrations about its axis. The motion of the fluid is described by Navier-Stokes equations for the axisymmetric case. The stream function is represented by a generalized Fourier series. The small parameter is the ratio of the vibration amplitude to the radius of the external cylinder. Calculations carried out in the zeroth approximation produced the pattern of stream lines for various Reynolds numbers, vibration amplitudes, and ratios of external and internal radii. The mixing intensity was found to increase substantially with the reduction of the gap between the cylinders, whereas variation of the ratio of the vibration amplitude to the Reynolds number did not produce marked qualitative changes. The fluid flow in this system generates a contraction semigroup, which makes it possible to derive the ergodicity criterion for the stream function.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 35–39, 1986.     

Extracting energy from Vortex-Induced Vibrations: A parametric study

Here, Vortex-Induced Vibrations (VIVs) of a circular cylinder are analyzed as a potential source for energy harvesting. To this end, VIV is described by a one-degree-of-freedom model where fluid forces are introduced from experimental data from forced vibration tests. The influence of some influencing parameters, like the mass ratio m^∗ or the mechanical damping ζ in the energy conversion factor is investigated. The analysis reveals that: (i) the maximum efficiency η_M is principally influenced by the mass-damping parameter m^∗ζ and there is an optimum value of m^∗ζ where η_M presents a maximum; (ii) the range of reduced velocities with significant efficiency is mainly governed by m^∗, and (iii) it seems that encouraging high efficiency values can be achieved for high Reynolds numbers.     

Vibration optimization of an infinite circular AT-cut quartz resonator with ring electrodes

This paper presents the thickness-shear (TSh) vibration modes of an infinite circular AT-cut quartz resonator with ring electrodes. By application of 2D scalar differential equations derived by Tiersten and Smythe, we obtain the resonant frequencies and vibration amplitude distributions of thickness-shear modes in the resonator. The theoretical results have been verified in commercial FEM software COMSOL. Through numerical examples, we illustrate that the distribution of displacement fields in the center part of the ring electrode is adjustable. Furthermore, we optimize the size of the electrodes and the mass ratio of the electrode to the plate, in order to achieve a nearly uniform displacement distribution and mass sensitivity of the resonator. These results can be a theoretical guidance for design and optimization of sensors based on quartz resonators.     

井下钻柱纵向横向耦合振动模型建立与数值分析

针对井下钻柱运动的复杂性,基于动力学理论,建立了井下钻柱纵向和横向耦合振动的数学模型,并进行数值求解及分析.根据井下钻柱的实际工况,以整个井下钻柱为研究对象,提出了钻柱纵向和横向耦合振动的动力方程,并利用解析法和无量纲法分别求解出其动刚度和动阻尼的表达式,以及钻柱前两阶振动的固有频率.分析结果表明:当井下钻柱振动频率增大时,其动刚度呈幅值衰减的周期性变化,而其动阻尼呈幅值增强的周期性变化;井下钻柱长度和横截面面积越大,其动刚度和动阻尼的幅值越小;井下钻柱的Poisson(泊松)比对其振动的动刚度、动阻尼和前两阶固有频率没有影响;同时,井下钻柱的第二阶固有频率始终大于第一阶固有频率.该文的研究方法和模型为井下钻柱钻具分析和结果优化提供了理论参考和实际意义.     

Development of a finite element solution module for the analysis of the dynamic behavior and balancing effects of an induction motor system

The study developed a multipurpose finite element solution module with the theoretical groundwork originated from principles of rotordynamics. This module is capable of solving many of the related rotating machine problems such as of the high speed gas bearing spindles and the electric machines. The goal of this paper is to utilize the developed solution module in investigating various aspects of the vibration behavior of an induction motor system for solving its failure problem of the shaft. Some of the crucial factors to the quality and performance of the motor, such as the vibration amplitude as resulted from the bearing wear, damping effects, mass unbalance, and the passing of system resonance critical speeds, are all investigated in the study. An efficient dual-rotor model is verified to have excellent accuracy when comparing the calculated frequency response function (FRF) with that from modal testing. The results of the transient orbit analysis indicate that the bearing stiffness and damping dominates the vibration amplitude remarkably. The effects both from the bearing damping as well as from the clamping–damping between the silicon steel core and the rotating shaft are all examined. It is noticed that the bearing damping plays the major role in the restraint of the vibration amplitudes of the rotor. For the analysis of vibration suppression with different eccentricities of the unbalanced masses, it is found that the adding of balance masses will normally suppress the vibration amplitude effectively until the point where an optimum amount that causes the minimum balanced vibration amplitudes is observed. Both the qualitative and quantitative analyses for the effectiveness of the balance mass added with different eccentricity ratios are studied. Thus, the critical adding mass ratio (i.e. the adding mass ratio at the minimum balanced amplitude factor) can also be predicted through its linear relationship with the eccentricity ratio. Based on all the findings through the study, it is concluded that the approach not only can solve the realistic shaft vibration failure problems of a motor and the demonstrated processes are also believed to be able to help the designers to have better command of motor performance at the system design stage.     

Modeling large amplitude vibration of pretwisted hybrid composite blades containing CNTRC layers and matrix cracked FRC layers

A modeling of the large amplitude free vibration of pretwisted hybrid composite blades is studied by considering the laminated structure which is composed of carbon nanotube reinforced composite (CNTRC) layers and matrix cracked fiber reinforced composite (FRC) layers. Two assumptions are made to facilitate this vibration study of hybrid nanocomposite: (1) CNTs are distributed across the layer thickness uniformly or functionally graded, and (2) the parallel slit matrix cracks disperse in the matrix homogeneously. Based on the theory of differential geometry, a novel shell model for pretwisted hybrid nanocomposites blade is developed. The von Kármán strains are adopted to capture the geometrically nonlinear behaviors of blades. The established governing equations are solved accurately and efficiently via the IMLS-Ritz method. The proposed numerical model is verified by making comparison studies and then the influence of crack density, pretwisted angle, CNT distribution and volume fraction, aspect ratio, width-to-thickness ratio, and ply-angle on the large amplitude vibration characteristics of matrix cracked pretwisted hybrid composite blade are scrutinized systematically. The present study serves as a useful benchmark to researchers who intend do further research in this topic.