Space-time objective decomposition of vortex equations and mechanism analysis of subtropical high abnormal activities

To analyze the dynamic mechanism of unusual activities of the subtropical high, the space-time varible separation of the partial differential vortex equations is carried out with Galerkin methods based on the heat force and the whirl movement dissipation effect. Aiming at the subjective and man-made conventional method of choice in the space basis functions, we propose to combine the empirical orthogonal function （EOF） analysis with the genetic algorithm to inverse the space basis functions from the actual sequence of fields. A group of trigonometric functions are chosen as a generalized space basis function. With the least-squares error of the basis function and EOF typical fields, and with the complete orthogonality of basis functions, we can get the dual-bound function. A genetic algorithm is then introduced to carry out surface fitting and coefficient optimization of the basis function. As a result, the objective and reasonable constant differential equation of the subtropical high is obtained by inversion. Finally, based on the obtained nonlinear dynamics model, the dynamic behavior and mechanism of the subtropical high is analyzed and discussed under the influence of heat force. We find that solar radiation and zonal differences in land and sea are important factors impacting the potential field and flow field changes of the subtropical areas. These factors lead to strength changes of the subtropical high and medium-term advance/retreat activities. The former is a gradual change, while the latter shows more break characteristics. Meaningful results are obtained in the analysis.     

General dynamic equation and dynamical characteristics of viscoelastic Timoshenko beams

In this paper, a governing differential equation of viscoelastic Timoshenko beam including both extension and shear viscosity is developed in the time domain by direct method. To measure the complex moduli and three parameters of standard linear solid, the forced vibration technique of beam is successfully used for PCL and PMMA specimens. The dynamical characteristics of viscoelastic Timoshenko beams, especially the damping properties, are derived from a considerable number of numerical computations. The analyses show that the viscosity of materials has great influence on dynamical characteristics of structures, especially on damping, and the standard linear solid model is the better one for describing the dynamic behavior of high viscous materials.     

结构动力可靠度的重要抽样法

重要抽样法是蒙特卡洛数值模拟方法中的一种重要的方差缩减技术,目前重要抽样法在工程结构可靠度计算中的应用主要集中于静力问题。本文分析了动力可靠度蒙特卡洛方法的特点,提出了在结构动力可靠度问题中应用重要抽样法的方法,并针对白噪声荷载,给出了选择重要抽样函数的方法和重要抽样函数的具体表达式。理论和数值分析表明,本文所提出的重要抽样法应用于结构动力可靠度计算是可行的。     

Applying local model approach for tidal prediction in a deterministic model

In recent years, a practice of tidal prediction based on a deterministic model or by a time series forecasting model has been established. A deterministic model can predict tidal movement and capture the dynamics of the flow pattern over the entire domain. However, due to the simplification of model settings and near shore effects, the accuracy of the numerical model can diminish. Time series forecasting is capable of capturing the underlying mechanism that may not be revealed in the deterministic model simulation. However, such data‐driven forecast fails to maintain accuracy with the progress of forecast horizon. In this paper, a scheme that combines the advantages of these two methods is introduced. The model errors are forecasted to different time horizons using a data‐driven approach, and are then superimposed on the simulation results in order to correct the model output. Based on the proposed method, it is found that the accuracy is significantly improved with more than 50% of the errors removed on the average. Copyright © 2008 John Wiley & Sons, Ltd.     

基于非线性状态空间辨识的气动弹性模型降阶

高维、非线性气动弹性系统的模型降阶是当前气动弹性力学与控制领域的研究热点之一.然而国内外现有的非线性模型降阶方法仍存在辨识算法复杂、精度有待提高等问题.本研究提出了一种基于非线性状态空间辨识的跨音速气动弹性模型降阶方法. 首先,该方法基于非定常空气动力的单位脉冲响应数据,采用特征系统实现算法对非线性状态空间模型的线性动力学部分进行系统辨识. 其次,引入状态和控制输入的非线性函数, 采用优化算法对非线性函数的系数矩阵进行优化,进而得到考虑非线性效应的空气动力降阶模型.为了验证该降阶模型在预测跨音速气动弹性力学行为的精确性,本文以三维机翼为研究对象,分别从基于非线性降阶模型的气动力辨识、跨声速颤振边界计算和极限环振荡预测三方面进行了算例验证,并与现有的模型降阶方法进行了对比, 进一步说明本文所提出方法的有效性.研究结果表明, 该降阶模型对上述三类问题的计算精度与直接流-固耦合方法相吻合,可用于高效预测飞行器跨声速气动弹性力学行为.      

Study on application of random walk method to calculate water exchange in large-scale bay

The water exchange matrix is an efficient tool to study the water exchange among the sub-areas in large-scale bays. The application of the random walk method to calculate the water exchange matrix is studied. Compared with the advection-diffusion model, the random walk model is more flexible to calculate the water exchange matrix. The forecast matrix suggested by Thompson et al. is used to evaluate the water exchange characteristics among the sub-areas fast. According to the theoretic analysis, it is found that the precision of the predicted results is mainly affected by three factors, namely, the particle number, the generated time of the forecast matrix, and the number of the sub-areas. The impact of the above factors is analyzed based on the results of a series of numerical tests. The results show that the precision of the forecast matrix increases with the increase of the generated time of the forecast matrix and the number of the particles. If there are enough particles in each sub-area, the precision of the forecast matrix will increase with the number of the sub-areas. Moreover, if the particles in each sub-area are not enough, the excessive number of the sub-areas can result in the decrease of the precision of the forecast matrix.     

滞变智能隔震结构的序列最优控制算法

将地震波简化为一系列脉冲,在每个时间步长上重新构造控制目标函数,建立了一种新的时域内的结构振动最优控制算法,并在滞变模型的智能隔震结构中用状态转移法加以实现.文中采用Bouc-Wen模型描述结构恢复力,并利用等效线性化方法处理非线性运动方程,分别导出了状态反馈和输出加权的两种表达式.文末选用作者承担设计过的实际隔震建筑中的一个单体工程作为算例,比较了输入三种不同地震波时各种算法的控制效果.结果表明,在相同控制能量下,本文算法对滞变结构能有效地削减响应峰值,综合性能优于现有的两种时域内的结构最优控制算法.     

方形钢筋混凝土板的近场抗爆性能

为了探讨钢筋混凝土板在爆炸载荷作用下的抗爆性能,对方形钢筋混凝土板在单向支撑条件下进行了近场爆炸加载实验,实验中采取TNT装药对钢筋混凝土板进行加载.并利用AUTODYN软件采用流固耦合算法,建立了混凝土和钢筋三维分离式实体模型,对钢筋混凝土板的动态响应过程进行数值模拟,且考虑应变率对钢筋和混凝土材料的动态本构特性的影...     

基于混沌神经网络理论的城市地面沉降量预测模型

通过分析城市地面沉降量时间序列的非线性动力学系统,认为该时间序列具有混沌特性。在此基础上,通过相空间重构的方法建立了用于城市地面沉降量预测的混沌神经网络模型;并利用此模型对高桥地面沉降量进行了预测,并和实际监测沉降量进行了比较,最大绝对预测误差为1. 7,预测的平均误差为0. 0833,研究结果表明,应用混沌神经网络模型进行城市沉降预测是可行、精确的。     

刚性杆-弹簧摆模型复杂动力学特性的数值仿真

建立一种刚性杆-弹簧摆刚柔耦合强非线性动力学系统模型,给出了无量纲的动力学微分方程．该模型同时存在小幅度快速振荡和大范围慢速摆动的快、慢双时间尺度变量．针对工程中此类系统数值求解容易产生的刚性问题,采用一种三次Hermite插值精细积分法进行数值计算．将频率比、摆长比和初始摆角作为控制参数,研究刚性杆-弹簧摆刚柔耦合系统快、慢变量的复杂动力学行为．通过数值仿真分析,发现系统在不同的控制参数组合下呈现出混沌运动状态,并给出了与系统运动状态相关的控制参数范围,为复杂的刚柔耦合多体系统的设计与数值分析提供了参考．     

An efficient goal‐based reduced order model approach for targeted adaptive observations

An efficient adjoint sensitivity technique for optimally collecting targeted observations is presented. The targeting technique incorporates dynamical information from the numerical model predictions to identify when, where and what types of observations would provide the greatest improvement to specific model forecasts at a future time. A functional (goal) is defined to measure what is considered important in modelling problems. The adjoint sensitivity technique is used to identify the impact of observations on the predictive accuracy of the functional, then placing the sensors at the locations with high impacts. The adaptive (goal) observation technique developed here has the following features: (i) over existing targeted observation techniques, its novelty lies in that the interpolation error of numerical results is introduced to the functional (goal), which ensures the measurements are a distance apart; (ii) the use of proper orthogonal decomposition (POD) and reduced order modelling for both the forward and backward simulations, thus reducing the computational cost; and (iii) the use of unstructured meshes. The targeted adaptive observation technique is developed here within an unstructured mesh finite element model (Fluidity). In this work, a POD reduced order modelling is used to form the reduced order forward model by projecting the original complex model from a high dimensional space onto a reduced order space. The reduced order adjoint model is then constructed directly from the reduced order forward model. This efficient adaptive observation technique has been validated with two test cases: a model of an ocean gyre and a model of 2D urban street canyon flows. Copyright © 2016 John Wiley & Sons, Ltd.     

Hybrid stress analysis of vibrating plates using holographic interferometry and finite elements

The work reported herein is concerned with an investigation of the potential of mating time-average holography and static-finite-element analysis (a ‘hybrid’ stress-analysis technique) in solving dynamic problems. The model studied is a vibrating thin rectangular cantilever plate. Realtime holography was used to locate natural vibrating modes of the plate. Experimental data were smoothed to remove scatter using a spline-like procedure in one or two dimensions, as applicable. Two methods of smoothing the experimental displacement data used in the hybrid procedure were considered. The first involved preprocessing (smoothing) the data before they were incorporated into the numerical model, while the second involved smoothing the data as part of the solution process. In both instances the amount of smoothing was specified by the user. The first and fourth vibrational modes were investigated. The results were compared to a NASTRAN dynamic solution and to a Ritz method series solution with very good results.     

Restoring force and dynamic loadings identification for a nonlinear chain-like structure with partially unknown excitations

Most of the currently employed vibration-based identification approaches for structural damage detection are based on eigenvalues and/or eigenvectors extracted from dynamic response measurements, and strictly speaking, are only suitable for linear system. However, the inception and growth of damage in engineering structures under severe dynamic loadings are typical nonlinear procedures. Consequently, it is crucial to develop general structural restoring force and excitation identification approaches for nonlinear dynamic systems because the restoring force rather than equivalent stiffness can act as a direct indicator of the extent of the nonlinearity and be used to quantitatively evaluate the absorbed energy during vibration, and the dynamic loading is an important factor for structural remaining life forecast. In this study, based on the instantaneous state vectors and partially unknown excitation, a power series polynomial model (PSPM) was utilized to model the nonlinear restoring force (NRF) of a chain-like nonlinear multi-degree-of-freedom (MDOF) structure. To improve the efficiency and accuracy of the proposed approach, an iterative approach, namely weighted adaptive iterative least-squares estimation with incomplete measured excitations (WAILSE-IME), where a weight coefficient and a learning coefficient were involved, was proposed to identify the restoring force of the structure as well as the unknown dynamic loadings simultaneously. The response measurements of the structure, i.e., the acceleration, velocity, and displacement, and partially known excitations were utilized for identification. The feasibility and robustness of the proposed approach was verified by numerical simulation with a 4 degree-of-freedom (DOF) numerical model incorporating a nonlinear structural member, and by experimental measurements with a four-story frame model equipped with two magneto-rheological (MR) dampers mimicking nonlinear behavior. The results show the proposed approach by combining the PSPM and WAILSE-IME algorithm is capable of effectively representing and identifying the NRF of the chain-like MDOF nonlinear system with partially unknown external excitations, and provide a potential way for damage prognosis and condition evaluation of engineering structures under dynamic loadings which should be regarded as a nonlinear system.     

Dynamical randomicity and predictive analysis in cubic chaotic system

The dynamical randomicity and grey prediction in cubic chaotic system will be studied in this paper. These stochastic symbolic sequences bear three features. The distribution of frequency, inter-occurrence times, the first passage time, the rth passage time and the ordinal passage time are discussed separately. By using transfer probability of Markov chain (MC), one obtains analytic expressions of generating functions in three-probabilities stochastic wander model, which can be applied to all three symbolic systems. The visitation density function of cubic map will also be resolved. Especially, after introducing grey system theory, one is mainly using GM(1,1) model to forecast data sequences, and the usual forecast precision is approximately 90%. In the symbolic prediction of cubic chaotic dynamical system, the precision of grey prediction certainly will decrease as the length of symbolic sequence is increasing. But in this place we have found a generating rule that may realize chaotic synchronization at least in short and medium terms, and we can analyze and forecast in this way.     

基于黎曼几何的非线性振子动力学分析递推解析算法

基于黎曼几何和变分原理，推导了黎曼流形上非线性耗散动力系统的二阶微分动力学方程，并运用流形收缩的概念将动力学方程离散化，进而建立了相应的递推求解格式。选取3个自治非线性阻尼振子系统，分别采用递推解析算法和龙格库塔法求解微分动力学方程，并比较分析了不同的时间步长下两种算法的计算耗时。结果表明，与龙格库塔法相比，基于黎曼几何的递推算法不仅能得到每一时步的解析表达式，而且计算耗时短，计算效率高。基于黎曼流形的动力学方程递推算法为非线性动力学系统的解析求解提供了新思路。     

转子系统非线性动力学DEM建模研究

将DEM方法引入转子系统非线性动力学的分析计算,对其建模过程和有关本构关系,作了比较详尽的介绍。该模型可用于碰摩、弯曲振动和扭转振动等转子系统的大部分动力学和运动学问题分析计算,不仅适用于单跨转子系统,也适用于多跨转子系统,尤其是在碰摩计算时,可考虑其摩擦特性随时间历程而变的特点,从而使分析计算更加接近实际情况。     

PATH INTEGRAL SOLUTION OF NONLINEAR DYNAMIC BEHAVIOR OF STRUCTURE UNDER WIND EXCITATION

IntroductionThe dynamic behavior of the nonlinear structure under wind excitation has beenobserved very complicated.Taking guyed masts as an example,only a few collapsingaccidents occurred under extreme atmospheric conditions[1],many took place under mild…     

Attractor Reconstruction with Principal Components Analysis: Application to Work Flows in Hierarchical Organizations

Explored several procedural questions in the use of the principal components technique for filtering time series data and reconstructing attractors in two or more dimensions. Data originated from an earlier study on work flows in experimental hierarchical organizations. The reconstructed time series and attractors were evaluated alongside a nonlinear regression modeling approach for assessing the dynamical properties of data. The results showed that, if the nonlinear function representing the time series is initially poorly fitted, principal components filtering will probably help to identify a nonlinear structure insofar as it has been fed enough data to capture the complexity of the time series of events. The relative merits of the eigenvalue 1.00 criterion and the scree test for determining the correct number of components were also addressed. Oblique rotation procedures are recommended.     

一维流体饱和粘弹性多孔介质层的动力响应

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论，在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下，建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型，利用Laplace变换，求得了原初边值问题在变换空间中的解析解，并利用Laplace逆变换的Crump数值反演方法，得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应，分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明，与不可压流体饱和弹性多孔介质相同，不可压流体饱和粘弹性多孔介质中亦只存在一个纵波，并且固相骨架的粘性对动力行为有显著的影响。     

Semi-analytical solution for a system with clearance nonlinearity and periodic excitation

Many dynamical systems such as gears, tire-pavement, automotive brakes, and cam-follower have clearance nonlinearity and excitation, which are periodic in nature. It is essential to accurately predict the steady-state response of these systems using contact-mechanics-based model for understanding their nonlinear dynamic behavior. Among the methods available to theoretically solve the system’s nonlinear governing equation(s), a semi-analytical technique such as the harmonic balance method (HBM) is preferred over numerical approaches for various reasons, including accuracy. An HBM formulation that can predict the fundamental, sub-, and super-harmonic solutions is presented here. As multiple variants of HBM exist in the literature, this work focuses on comparatively evaluating the most appropriate variant for the system under consideration. Since the system has multiple discontinuities in terms of contact stiffness and damping forces, these have to be smoothed precisely to be utilized in the HBM. Hence, a novel smoothing function was proposed and evaluated against other existing smoothing functions in literature based on various criteria. Next, the most applicable HBM variant was selected with reference to steady-state solutions from numerical methods. The predictions from the selected HBM variant were validated against the results furnished in the literature for a similar system. Finally, the nonlinear frequency response of the system with multiple discontinuities was estimated using the selected HBM and found to be in good agreement with numerical results.