FIRST-PASSAGE FAILURE OF PREISACH HYSTERETIC SYSTEMS

The first-passage failure of a single-degree-of-freedom hysteretic system with non- local memory is investigated. The hysteretic behavior is described through a Preisach model with excitation selected as Gaussian white noise. First, the equivalent nonlinear non-hysteretic sys- tem with amplitude-dependent damping and stiffness coefficients is derived through generalized harmonic balance technique. Then, equivalent damping and stiffness coefficients are expressed as functions of system energy by using the relation of amplitude to system energy. The stochastic aver- aging of energy envelope is adopted to accept the averaged It5 stochastic differential equation with respect to system energy. The establishing and solving of the associated backward Kolmogorov equation yields the reliability function and probability density of first-passage time. The effects of system parameters on first-passage failure are investigated concisely and validated through Monte Carlo simulation.     

Random Vibration of SMA Systems via Preisach Formalism

Interest in shape memory alloys (SMA) applications has increased dramatically in recent years. The primary problem in studying systems endowed with SMA devices involves quantifying their mechanical behavior. A most promising tool for this task is the Preisach model, which, due to its abstract nature, is extremely versatile for capturing various hysteretic phenomena present in SMA. In this paper a procedure to calibrate the Preisach model to fit available experimental data is employed first. Then the random responses of SMA systems are investigated by focusing on the numerical implementation of the Preisach model. A version of the stochastic averaging technique is used for this purpose. The probability density function of the amplitude and the power spectral density of the response are determined. Also, the probability density function of the response process is estimated. The analytical results are found in good agreement with those derived by a pertinent Monte Carlo study. Obviously, the methodology described herein can be applied for the study of other hysteretic systems, such as mechanical joints, provided that adequate calibration of the Preisach model has been performed a priori.     

Direct specturm analysis of the state space for random vibration of MDOF linear damped system

This paper proceeds from the general case of the unsymmetric linearized multi-degrees of freedom (MDOF) systems. By adopting the general complex modal theory of the state space, the response analysis for a system subjected to random excitation of the same source is carried out using as a kind of direct spectrum analysis method in frequency domain. With the input of power spectral density function given, the explicit expression of the power spectral density function matrix of the output response can be obtained. By taking Fourier inverse transform, the integrated expressions of the correlation function matrix and of the spectrum moment matrix are obtained. Comparing with the time domain method, this method enjoys the merit of visualization and avoids the procedure of transformation from the obtained response correlation function to be solved for the output spectrum utilizing Fourier transform. This paper has extended the application range of the traditional frequency domain analysis method. The mean square values and variety of statistical values can be obtained conveniently. This method and the time domain method are different in approach but equally satisfactory in their results. The project is supported by National Natural Science Foundation of China and National Education Commission Science Foundation of China     

On the local average of random field in stochastic finite element analysis

The distinguishing feature of stochastic finite element analysis is that it involves the discretization of the parameter space of random fields of material properties, the geometry of structure and / or the loads. It is shown in earlier investigations that a reasonable procedure of discretization is to take the local averages of the random fields on each element. In the present paper the formulae for the covariance of the local averages of a homogeneous random vector field on rectangular elements are generalized by relaxing the condition. For an inhomogeneous random field and /or non-rectangular elements, a procedure of using Gaussian quadrature to evaluate the means and covariances of the local averages is proposed. Thus, the stochastic finite element method (SFEM) based on the local averages of random fields is adapted to a structure with irregular shape and / or inhomogeneous random fields. The effects of the mesh geometry, the ratio of element size to the correlation scale as well as the number of Gaussian quadrature points on the convergence of SFEM are discussed. It is found that even better results could be obtained by utilizing appropriate Gaussian quadrature instead of exact local average.Project supported by National Natural Science Foundation of China.     

On delay-dependent robust exponential stability of stochastic neural networks with mixed time delays and Markovian switching

This paper deals with the global exponential stability analysis problem for a general class of uncertain stochastic neural networks with mixed time delays and Markovian switching. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. The main purpose of this paper is to establish easily verifiable conditions under which the delayed stochastic neural network is robustly exponentially stable in the mean square in the presence of parameters uncertainties, mixed time delays, and Markovian switching. By employing new Lyapunov–Krasovskii functionals and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria for the robust exponential stability, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. The criteria derived are dependent on both the discrete time delay and distributed time delay, and, are therefore, less conservative. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria. This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the National Natural Science Foundation of China under Grant 60774073, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the Natural Science Foundation of Jiangsu Education Committee of China under Grant 06KJD110206, the Scientific Innovation Fund of Yangzhou University of China under Grant 2006CXJ002, and the Alexander von Humboldt Foundation of Germany.     

Chaotic motion of a nonlinear thermoelastic elliptic plate

In the paper the nonlinear dynamic equation of a harmonically forced elliptic plate is derived, with the effects of large deflection of plate and thermoelasticity taken into account. The Melnikov function method is used to give the critical condition for chaotic motion. A demonstrative example is discussed through the Poincaré mapping, phase portrait and time history. Finally the path to chaotic motion is also discussed. Through the theoretical analysis and numerical computation some beneficial conclusions are obtained. Foundation item: the National natural Science Foundation of China (19672038); the Natural Science Foundation of Shanxi Provence (1880342).     

非高斯随机激励下滞迟系统响应与首次穿越失效

针对由有界噪声、泊松白噪声和高斯白噪声共同构成的非高斯随机激励,通过Monte Carlo数值模拟方法研究了此激励作用下双线性滞迟系统和Bouc-Wen滞迟系统这两类经典滞迟系统的稳态响应与首次穿越失效时间。一方面,分析了有界噪声和泊松白噪声这两种分别具有连续样本函数和非连续样本函数的非高斯随机激励,在不同激励参数条件下对双线性滞迟系统和Bouc-Wen滞迟系统的稳态响应概率密度、首次穿越失效时间概率密度及其均值的不同影响;另一方面,揭示了在这类非高斯随机激励荷载作用下,双线性滞迟系统的首次穿越失效时间概率密度将出现与Bouc-Wen滞迟系统的单峰首次穿越失效时间概率密度截然不同的双峰形式。     

Effects of local non-uniform particle temperature on radiative heat transfer in particulate systems

In many high-temperature particulate systems, the temperature differences between particles in some local sites are often large. Due to the nonlinear nature of the Stefan-Boltzmann law, the average radiative source term deviates significantly from the radiative source term based on the average particle temperature. In this paper, a Gaussian probability density function is used to simulate the distribution of particle temperature. The discrete ordinates method is selected to solve the radiative heat transfer in particulate systems and the axial radiative heat flux is calculated. The results show that, when the non-uniform degree of local particle temperature is large, calculating the radiative source term by local average particle temperature will result in large errors in the calculation of radiative heat transfer, especially in the absorption-dominated case. The author acknowledges the supports provided by Fok Ying Tung Education Foundation (No. 71053) and National Natural Science Foundation of China (No. 50176011) for this work.     

TheC k instability of navier-Stokes equation appending polynomials of unknown functions

Applying the theory of stratification, the solution space structure about a class of deformed Navier-Stokes equation isdetermined. It is proved that such kind of equation has no C^k (k≥2) stable solution by the fact that the strate transversale is a null set. Foundation item: the National Natural Science Foundation of China (19971054), Shanghai Natural Science Foundation (99ZA14034) Biography: HE You-hua (1960-)     

POLY-SCALE REFINABLE FUNCTION AND THEIR PROPERTIES

Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of solution functionφof poly-scale refinable equation with integer dilation factor a are established. Some properties of poly-scale re-finable function are discussed. Several examples illustrating how to use the method to construct poly-scale refinable function are given.     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOWWATER EQUATIONS INCLUDING CURRENT AND SILTSEDIMENTATION （Ⅱ）——THE DISCRETE-TIMECASE ALONG CHARACTERISTICS

The mixed finite element(MFE) methods for a shallow water equation systemconsisting of water dynamics equations, silt transport equation, and the equation of bottomtopography change were derived. A fully discrete MFE scheme for the discrete-time alongcharacteristics is presented and error estimates are established. The existence andconvergence of MFE solution of the discrete current velocity, elevation of the bottomtopography, thickness of fluid column, and mass rate of sediment is demonstrated.     

Experimental study on turbulent features in the negative transport region of asymmetric plane channel flow

Turbulent features of streamwise and vertical components of velocity in the negative transport region of asymmetric plane channel flow have been studied experimentally in details. Experiments show that turbulent fluctuations in negative transport region are suppressed, and their probability distributions are far from Gaussian. Besides, the skewness factors attain their negative maxima at the position of the maximum mean velocity, whereas the flatness factors attain their positive maxima at the same position. The project supported by the National Natural Science Foundation of China (19872043)     

Some issues of turbulence statistics

The issue of dropping the random forcef _i and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and Kukharkin, are discussed. According to the mean-square estimation method, the random forcef _i should be dropped in the error expression of the LFP (Langevin-Fokker-Planck) model. However,f _i is not neglected, its effect has been taken into account by the variational approach. In order to optimize the perturbation solution of the Liouville equation, the LFP model requires that the basic variable is as near to Gaussian as possible. Hence, the velocity, instead of the vorticity, should be chosen as the basic variable in the three-dimensional turbulence. Although the LFP model and the zero-order Gaussian term of PDF (probability density function) imply whiteness assumption (zero correlation time off _i ), the higher-order non-Gaussian terms of PDF correspond to the nonwhiteness of turbulence dynamics, the variational approach does calculate the nonwhiteness effect properly. The work is supported by the National Basic Research Program “Non-linear Sciences” and the National Natural Science Foundation of China     

基于state-space-split法的滞回非线性系统随机动力响应分析

采用SSS(state-space-split)法,建立了引入Bouc-Wen滞回模型的杜芬非线性系统在高斯白噪声激励下的概率密度函数(PDF)的近似求解方法,分析了其随机动力响应变化规律.首先,将Bouc-Wen滞回模型引入杜芬非线性系统,分别考虑非线性系统中的几何非线性和材料非线性对动力响应的影响.随后,对该模型进...     

Analysis of saltation characteristics of bed-load transport in flowing water

The study of bed-load transport is of great significance both in theory and in practice. This paper discusses the saltation of bed-load solid grains in flowing water. Experiments and theoretic analysis have been made by means of high-speed photographing and advanced data processing technique with a combined method based on mechanical and statistical theories. It indicates that the saltation is the main form of the bed-load transport under ordinary flowing conditions. In the meantime, taking successive saltation as the model of bed-load transport, systematic analysis has been made with regard to the kinematic properties and mechanism of saltation. The statistical analysis shows that the probability density functions of the relative height and length of saltation are in conformity with Γ-type distribution, while the probability density functions of the relative velocities of saltation are in conformity with the Gaussian distribution. The project supported by National Natural Science Foundation of China     

Bifurcation of the electromechanically coupled subsynchronous torsional oscillating system with hysteretic behavior

In subsynchronous resonance (SSR) systems where shaft systems of turbine-generator sets are coupling with electric networks, Hopf bifurcation will occur under certain conditions. Some singularity phenomena may generate when the hysteretic behavior of couplings in the shaft systems in considered. In this paper, the intrinsic multiple-scale harmonic balance method is extended to the nonlinear autonomous system with the non-analytic property, and the dynamic complexities of the system near the Hopf bifurcation point are analyzed. The project supported by the National Natural Science Foundation of China (as a key project) and the State Education Committee Pre-research Foundation.     

A Simple Fast Method in Finding Particular Solutions of Some Nonlinear PDE

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Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.     

The 3-D stress intensity factor for a half plane crack in a transversely isotropic solid due to the motion of loads on the crack faces

Three-dimensional analysis of a half plane crack in a transversely isotropic solid is performed. The crack is subjected to a pair of normal point loads moving in a direction perpendicular to the crack edge on its faces. Transform methods are used to reduce the boundary value problem to a single integral equation that can be solved by the Wiener-Hopf technique. The Cagniard-de Hoop method is employed to invert the transforms. An exact expression is derived for the mode I stress intensity factor as a function of time and position along the crack edge. Some features of the solution are discussed through numerical results. The project supported by the Guangdong Provincial Natural Science Foundation and the Science Foundation of Shantou University