理想塑性非线性弹簧支撑刚性圆柱涡激振动响应

应用尾流振子模型以及弱耦合算法的二维CFD数值方法,首次模拟了理想塑性非线性弹簧支撑刚性圆柱的涡激振动响应。CFD数值模拟与尾流振子经验模型预报结果一致显示:响应幅值超出非线性弹簧的极限位移后产生突变而迅速达到峰值,然后又逐渐变小;非线性弹簧情况下幅值峰值要低于线性,但出现在较低的流速。CFD数值方法还模拟到非线性弹簧支撑柱振动频率开始锁定泄涡频率,当振幅达到峰值后,随之锁定于静水固有频率附近。     

桥梁吊杆典型风致振动幅值响应质量阻尼效应研究

涡激共振与准定常驰振临界风速相近时,矩形杆件易发一种涡振与驰振耦合风致振动,区别于锁定区间涡振和发散性驰振,是一类响应幅值随风速的增加而线性增长的"软驰振"现象,质量、阻尼是影响耦合程度和估算幅值的关键参数。基于一组宽高比1.2∶1矩形截面杆件节段模型,通过调整模型系统等效刚度、等效质量和阻尼比,实现了Reynolds数一致情况下,相同质量不同阻尼比、相同阻尼比不同质量以及相同Scruton数不同质量、阻尼组合下风振响应对比试验研究。研究表明:耦合状态下,组成Scruton数的质量、阻尼参数对"软驰振"幅值响应的影响是独立的,权重相同;存在影响"软驰振"幅值响应Scruton数"锁定区间(12.4～30.6)","锁定区间"内,无量纲风速-幅值响应曲线线性斜率(Slope)不随Scruton数变化而变化,并存在一个使风致振动由耦合状态转变为非耦合状态的Scruton数"过渡区间(26.8～30.6)";修正了"软驰振"响应幅值估算经验公式,可用于类似工程杆件设计风速范围内的幅值预测。     

超高层建筑涡激振动不稳定现象分析

为了研究方截面超高层建筑涡激振动不稳定现象的特点及原因。进行了多自由度气弹模型风洞试验,对模型表面风压和模型顶部涡振位移进行了同步测量;定性分析了模型表面风压和涡振位移响应的瞬时频率及瞬时相位关系。结果表明:在共振临界风速下,涡振位移幅值并不稳定,涡振位移时程曲线表现为间歇性的"葫芦波";并且,模型表面风压频率和模型风振频率并不是一个恒定的值,二者时程的相位差一直处于波动状态,即没有构成一方"俘获"另一方的"锁定"现象;说明超高层建筑实际共振并不是理想的稳定共振,瞬时风压频率和位移频率的动态差异是涡激振动不稳定现象的直接原因。     

大跨度变截面连续钢箱梁桥涡激振动线性分析法

涡激力沿主梁跨向具有偏相关性,基于Scanlan涡激力经验线性模型,假定涡激振动风速下,整个梁段涡脱频率锁定,提出适用于变截面连续梁桥的三维涡激力经验线性模型,从而建立节段模型与变截面梁实桥之间涡激振动幅值之间的关系。通过变截面梁几个典型位置截面的节段模型风洞试验,获得描述整个变截面主梁三维涡激力经验线性模型等效参数,实现对整个变截面连续梁桥涡激振动响应的评估。并通过某典型的三跨变截面连续钢箱梁桥涡激振动风洞试验,验证了理论的有效性。     

圆柱体横流与顺流方向涡激振动耦合模型研究

基于尾流振子模型对刚性圆柱体在横流以及顺流方向涡激振动耦合模型进行了研究。首先建立了横流以及顺流方向考虑结构几何非线性的结构振子以及尾流振子模型,其次基于二阶精度中心差分格式对模型进行先离散后迭代求解,再次通过与他人实验结果进行对比验证了该数值模型的可靠性,最后对不同质量比、不同结构阻尼比以及不同几何非线性系数下圆柱体涡激振动响应振动幅值以及振动轨迹进行了分析。分析结果表明:随着质量比的增大,横流以及顺流方向的振动幅值均呈下降趋势,锁定区间宽度逐渐变窄。随着结构阻尼比的增大,横流以及顺流方向的振动幅值同样呈下降趋势,而锁定区间宽度逐渐变宽。随着折合速度的增加,结构振动轨迹依次出现斜"8"字形、"月牙"形以及正"8"字形。随着几何非线性系数的增加,横流以及顺流方向振动幅值从上分支进入低分支时的位移突降现象会变得越来越明显。     

Noor Ⅲ光热电站吸热塔气动阻尼研究

以位于非洲摩洛哥的Noor Ⅲ光热电站吸热塔为工程背景。加拿大西安大略大学风洞实验室的试验表明该吸热塔在设计风速下的位移值超过规范值的40%,该结构的涡振临界风速小于设计风速,且涡振区横风向响应起控制作用。据此,在已有光热电站吸热塔气弹模型的基础上进行了风洞试验;在不同结构阻尼比下采集了15 min的模型顶部加速度时程;运用随机减量法和广义卡尔曼滤波法得到气动阻尼比。结果表明:两种方法识别的气动阻尼比吻合较好;在不同加速度幅值处识别的总阻尼比具有随加速度幅值的增大先增大后减小的规律;根据ASCE/SEI7-10,在重现周期为50年,C类地貌条件下,风速6. 5 m/s时识别的气动阻尼比为负的最小。这些规律为涡振区横风向响应起控制作用的现象提供了合理的解释。     

高斯白噪声激励的阻尼耦合的两个杜芬-范德波振子的近似瞬态响应

研究受高斯白噪声作用下的非线性阻尼耦合的两个杜芬-范德波振子响应的近似瞬态概率密度。应用基于广义谐和函数的随机平均法,并将幅值的瞬态概率密度的近似解表示为拉盖尔正交基函数的级数和,其中系数是随时间变化的,用Galerkin法可得到幅值的近似瞬态概率密度,从而得到状态变量响应的近似瞬态概率密度,数值模拟结果表明该方法有很好的适用性及精度。     

桥梁涡激共振试验节段模型质量系统模拟与振幅修正方法

节段模型风洞试验是研究涡激共振风速锁定范围和最大振动幅值的一种重要手段。基于一个具有自激特性的经验线性涡激力模型,从涡激共振微分方程出发,推导了涡激共振试验节段模型质量系统模拟公式,并建立了相应的模型与实桥之间涡激共振幅值的换算关系,给出了涡激共振幅值的振型修正系数和阻尼修正系数公式。由此,通过合理的质量系统模拟和响应幅值换算,可在二维的涡激共振节段模型试验中考虑实桥的结构和振动的三维特性的影响。     

梯度风场中高耸结构涡致振动响应时程分析

采用两参数振子模型,考虑梯度风场中高耸结构的气-固耦合相互作用;运用片条理论和差分法,建立了烟囱涡激振动多自由度体系非线性方程。直接在时域中求解多自由度非线性涡振方程,准确地反映涡激振动的“锁定”和振幅峰值效应,并在时域中分析了烟囱结构发生涡致振动的响应幅值、临界风速范围及其影响因素。     

风-波浪荷载对海上风机地震响应的影响

建立广义单自由度模型,考虑运行、停机两种工作状态,揭示风-波浪荷载影响海上风机地震响应的机理。针对NREL 5MW单桩式海上风机,通过风-波浪统计关系确定波浪谱参数,采用FAST软件分析结构地震响应,验证初步分析结果的正确性,并探讨风-波浪影响海上风机地震响应的规律。结果表明:风-波浪作用的气动阻尼和动荷载效应使其显著影响海上风机地震响应;对于运行状态的海上风机,轮毂高度处平均风速等于额定风速时,支撑结构最危险;强震作用下,风-波浪作用减小泥面内力和塔顶位移幅值;弱震作用下,风-波浪荷载增大泥面内力和塔顶位移幅值。     

Modified higher-order wake oscillator model for vortex-induced vibration of circular cylinders

In the present study, a modified model is introduced to estimate the structural oscillation amplitude of a circular cylinder during lock-in in the vortex-induced vibration phenomenon. The modified model includes the same van der Pol term as in the classic model, while its coefficients are assumed to be variable. This modified model is utilized to bring about compliance between theoretical solution and experimental results. Then, a fifth-order aerodynamic term is added, and the coefficients are modified and optimized using a new straightforward solution method. Here, the displacement, velocity and acceleration coupling terms are used to solve the system of equations. The response of the coupled equations is assumed to be harmonic. A linear approach is adopted to simplify and derive the solutions algebraically. The results are plotted during lock-in for amplitude as a function of reduced velocity and for maximum structural oscillation amplitude versus Skop–Griffin parameter. Finally, these results are compared with those of the classic wake oscillator model. The present modified model evinces an exact compliance with experimental measurements regarding structural oscillation amplitude, lock-in range, some hysteresis and mass damping ratio attributes, and reduces sensitivity to the type of coupling term through adding the fifth-order damping term.     

Van der Pol oscillator with time variable parameters

In this paper, the analytical solving procedure of the oscillator with slow time variable mass is developed. The solution is based on the Jacobi elliptic function whose properties: frequency, amplitude and modulus are obtained according to the requirements given for the amplitude of the displacement and the amplitude of the velocity of vibration and also period of vibration. The suggested procedure is applied for the solution of the time variable Van der Pol oscillator. The limit value of the initial mass of the oscillator is determined which separates the case when the limit cycle motion occurs, and the case when the amplitude of vibration tends to zero independently of the initial displacement. A numerical example is considered. The analytical solution is compared with the numerically obtained one and it is concluded that they are in good agreement.     

Response analysis of Van der Pol oscillator subjected to harmonic and random excitations

The response of the Van der Pol oscillator subjected to combined harmonic and random excitations is investigated by a technique combining two excellent methods, namely the stochastic averaging method and the equivalent linearization method. The original equation is averaged by the stochastic averaging method at first. Then the resulting nonlinear averaged equations are linearized by the equivalent linearization method so that the equations obtained can be solved exactly by the technique of auxiliary function. The mean square response of the Van der Pol oscillator is computed algebraically and compared to the ones obtained by numerical simulation and by technique combining methods of stochastic averaging and equivalent non-linearization. The results show that the proposed technique gives a good prediction on mean square responses of the Van der Pol oscillator. In addition, the proposed technique can be applied to other nonlinear systems for it does not require any special conditions, and it can be improved by advanced optimization criteria of the equivalent linearization method.     

Stochastic averaging of quasi-linear systems driven by Poisson white noise

The averaged generalized Itô and Fokker–Planck–Kolmogorov (FPK) equations for single-degree-of-freedom (SDOF) quasi-linear systems driven by Poisson white noise are derived and the approximate stationary solutions of the averaged generalized FPK equations are obtained by using the perturbation method for four typical quasi-linear systems, i.e., van der Pol oscillator, Rayleigh oscillator, system with energy-dependent damping, and system with power law damping. The effectiveness and accuracy of the perturbation solution are assessed by performing appropriate Monte Carlo simulations. It is found that analytical and numerical results agree well and the effect of non-Gaussianity of the excitation process is not negligible for predicting the probability densities of total energy and displacement of quasi-linear systems in most cases.     

Simulation of evolution of the two cylinders plasma wake under the electric discharge influence

We consider a close wake behind a pair of cylinders at a Reynolds number of Re ~ 1000 defined by the cylinder diameter in the case of small aspect ratio of cylinders, H/D ≈ 3.5. The large-scale structure of such a wake represents a f low like two interacting Karman streets and it is modeled by two coupled Van der Pol oscillators. The mutual inf luence of closely located Karman streets is accounted for by nonlinear (of a general parabolic type) terms in the equations for oscillators. Moreover, the equations are generalized with allowance for explicit dependence of the oscillation frequency on its amplitude. Within the framework of this three-parametric model, five collective modes of the wake behind cylinders were found. In addition, there are the domains of model parameters where qualitatively different modes of intermittent wake exist.     

Response of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitations: A Path Integral approach based on Laplace’s method of integration

In this paper, an approximate analytical technique is developed for determining the non-stationary response amplitude probability density function (PDF) of nonlinear/hysteretic oscillators endowed with fractional element and subjected to evolutionary excitations. This is achieved by a novel formulation of the Path Integral (PI) approach. Specifically, a stochastic averaging/linearization treatment of the original fractional order governing equation of motion yields a first-order stochastic differential equation (SDE) for the oscillator response amplitude. Associated with this first-order SDE is the Chapman–Kolmogorov (CK) equation governing the evolution in time of the non-stationary response amplitude PDF. Next, the PI technique is employed, which is based on a discretized version of the CK equation solved in short time steps. This is done relying on the Laplace’s method of integration which yields an approximate analytical solution of the integral involved in the CK equation. In this manner, the repetitive integrations generally required in the classical numerical implementation of the procedure are avoided. Thus, the non-stationary response amplitude PDF is approximately determined in closed-form in a computationally efficient manner. Notably, the technique can also account for arbitrary excitation evolutionary power spectrum forms, even of the non-separable kind. Applications to oscillators with Van der Pol and Duffing type nonlinear restoring force models, and Preisach hysteretic models, are presented. Appropriate comparisons with Monte Carlo simulation data are shown, demonstrating the efficiency and accuracy of the proposed approach.     

van der Pol振子对高斯白噪声的响应

在过去20多年中,若干作者曾用不同方法研究过van der Pol振子对高斯白噪声的稳态响应,得到了不同甚至相反的结论。本文对此问题作了更为深入的研究,结果表明,在非线性不大时,随机平均法与等效非线性微分方程法给出良好的近似,而等效线性化法与高斯截断法给出错误的结论。     

Photorefractive optical lock-in vibration spectral measurement

An optical photorefractive frequency-domain method is described for measuring displacement amplitude and phase of vibrating surfaces. The method is applicable to diffusely scattering surfaces and usable in either a point-detection or imaging configuration. The method utilizes an optical lock-in approach to measure phase modulation of light scattered from continuously vibrating surfaces. Picometer displacement sensitivities have been demonstrated over a frequency range of 100 Hz to greater than 100 kHz. The response of the spectral method is independent of the vibration frequency above the photorefractive cutoff frequency. Two methods are described that produce a readout beam intensity that is a direct function of the vibration amplitude suitable for imaging.     

Detecting synchronization of self-sustained oscillators using wavelet analysis of univariate data for variable external drive frequency

A new method based on the continuous wavelet transform of univariate data is proposed for detecting the synchronization of a self-sustained oscillator under external drive action with linear frequency modulation. The efficacy of the proposed method is demonstrated in application to a model van der Pol oscillator and experimental physiological data.