地下结构荷载的广义反演方法

利用位移反分析方法进行地下结构荷载反演是行之有效的.本文针对地下结构荷载反算存在解的不唯一性和不稳定性,提出地下结构荷载的广义反演方法.借助奇异值分解和广义逆建立地下结构荷载反算的广义最小二乘解估计、广义最小范数解估计和广义最小方差解估计.     

(2+1)维广义Broer-Kaup方程的精确解

给出了一种新的辅助函数法,构造了一种新的形式的解,并给出了该新的辅助函数的一些新形式的周期解等,从而得出了所要求的偏微分方程的同宿孤立波解和带有周期的孤立波解.作为例子,求解了(2+1)维广义Broer-Kaup方程.显然该新的辅助函数法也可以求解其他多种类型的非线性发展方程,可见该方法是一种容易理解,计算简便,结果丰富的求解非线性偏微分方程的方法,并且具有一定的物理意义.     

参数激励下分段线性两尺度系统的分岔

对参数激励下分段线性系统进行了稳定性及分岔分析。以蔡氏电路系统为模型,在电阻中引入周期变化的部分,使得周期激励频率与系统固有频率之间存在量级差异,构造了两时间尺度非光滑动力系统。将该非自治系统化为广义自治系统,研究广义平衡点的稳定性,给出其失稳的分岔条件。在非光滑面处引用广义Jacobian矩阵进行非光滑分岔分析,得到了相应的分岔条件。     

具有非线性捕获的杂食性随机Lotka-Volterra模型周期解的存在性

研究了具有非线性捕获的杂食性随机Lotka-Volterrav模型,在较弱的条件下证明了解的存在唯一性,通过构造适当的Lyapuno函数,得到了随机模型周期解存在的充分条件,通过数值模拟验证了本文所得到的结论。结果表明,具有非线性捕获的杂食性随机Lotka-Volterra模型存在周期解。     

平面自治系统的周期解的存在性

本文研究一般平面自治系统ｘ＝ｐ（ｘ，ｙ）ｙ＝Ｑ（ｘ，ｙ）的非零周期解的存在性问题，获得了保证此系统存在非零周期解的充分条件，所得结果推广和改进一些已知结论。     

一类离散广义系统带有观测器的鲁棒无源控制

主要研究一类不确定离散广义系统,设计了有观测器的控制器作出恰当的李雅普诺夫函数,根据定义得到了一个线性矩阵不等式,用Schur定理的计算方法对线性矩阵不等式进行深入讨论和计算,最后得出了所得闭环离散系统鲁棒无源的充分条件,方法可行有效。     

一阶泛函微分方程变号周期解的存在性

利用不动点理论,讨论如下方程y′(t)=-a(t)y(t)+f(t,y(t-τ(t)))变号周期解的存在性,给出方程三个非零变号周期解的存在性,其中一个是正的,一个是负的,另一个是变号的。     

离散热传导方程稳态解的存在性

离散热传导方程的非退化稳态解的存在性对生产实践有着重要的意义,笔者构造了一个函数,使得带周期边界条件的一维离散热传导方程的解对应于此函数的临界点,然后通过使用Morse理论中的一些结果来讨论此函数的非退化临界点的存在性,从而得到了带周期边界条件的一维离散热传导方程至少存在两个非退化解的充分条件.最后通过一个例子说明所得的结论在具体的热传导方程中的应用.     

关于Hilbert空间中一类广义随机非线性变分不等式

介绍并研究了Hilbert空间中的Minty型广义随机非线性变分不等式问题,并在适当的条件和假设下,得到了这类广义非线性随机变分不等式和Stampacchia型广义随机非线性变分不等式的等价的结论;运用该结论,结合随机化的Banach压缩映像原理得到了关于这一类广义随机非线性变分不等式问题的一些新的随机解的存在性结果.     

二维Helmholtz方程Dirichlet问题的边界元解法

本文首先讨论了二维Helmho1tz方程Diricblet边值问题广义解的存在唯一性,然后得到了同时适合内问题和外问题的解的解积分表达式,并导出了与边值问題对应的第一类Fredholm边界积分方程.最后给出了与边界积分方程等价的变分方程的一种有限元近似解法.     

具滞后的离散广义系统的镇定

为了实现具滞后的离散广义系统的镇定 ,利用广义 Lyapunov方法设计了状态反馈镇定控制器 ,给出了一数值算例以验证文中定理的可行性 .     

Application of vector form intrinsic finite element on integrated simulation of wind turbine

Large wind turbine system is a periodic time‐varying system with many rigid‐flexible coupling bodies. It is difficult to deal with the singular stiffness matrix produced by the rotation of blades via the traditional finite element method. However, the vector form intrinsic finite element (VFIFE) method can effectively solve the geometric deformation of elastic continuum, the nonlinear or discrete constitutive model, the coupling motion continuum, and rigid body. In this study, a solver program of space beam element is developed by VFIFE method, and three typical examples are chosen to verify its accuracy. And then the integrated simulation of wind turbine system is established, and its dynamic response is analyzed. The natural frequencies of the turbine system, which are obtained by modal parameter identification, can agree well with the results obtained by traditional finite element method. The weighted amplitude wave superposition method and the proper orthogonal decomposition method as well as B‐spline surface interpolation are employed to obtain the wind time series of wind turbine under the normal operation condition. The wind‐induced dynamic response of wind turbine system is calculated by VFIFE method. The numerical results can reflect the periodic influence of gravity on the internal forces of blades and the interaction between blades and the tower.     

广义连续随机线性系统的状态估计问题

利用矩阵的奇异值分解理论 ,给出了广义连续随机线性系统的奇异值标准形式 ,基于标准形式 ,在两种情况下 ,将系统分解成两个子系统 ,通过估计子系统的状态 ,讨论了广义连续随机线性系统的状态估计问题 ,得到该系统状态的最优预测和滤波递推方程 .     

A parametric study of the free vibration analysis of rotating laminated cylindrical shells using the method of discrete singular convolution

This paper deals with the free vibration analysis of rotating laminated cylindrical shells. The analysis uses discrete singular convolution (DSC) technique to determine frequencies. Regularized Shannon's delta (RSD) kernel is selected as singular convolution to illustrate the present algorithm. The formulations are based on the Love's first approximation shell theory, and include the effects of initial hoop tension and centrifugal and coriolis accelerations due to rotation. The spatial derivatives in both the governing equations and the boundary conditions are discretized by the DSC method. Frequency parameters are obtained for different types of boundary conditions, rotating velocity and geometric parameters. The effect of the circumferential node number on the vibrational behaviour of the shell is also analysed. The analysis has been verified by comparing results with those in the literature and sufficient agreement is obtained.     

两种方法求组合KdV方程的新解

针对组合KdV方程,利用Jacobi椭圆函数展开法和修正的双曲正切函数展开法,分别研究了该类方程的椭圆余弦函数解、第三类Jacobi椭圆函数解和奇异行波解,给出了KdV方程新的周期解,所用方法同样可应用于求解其他类非线性方程.     

Discrete singular convolution method for buckling analysis of rectangular Mindlin plates

The discrete singular convolution (DSC) method is proposed for solving the elastic buckling problem of thick rectangular plates under a uniaxial compressive loading. To allow for the effect of transverse shear deformation in thick plates, the Mindlin plate theory has been adopted. The numerical results are checked against available analytical and other numerical solutions. It is found that the convergence of the DSC approach is very good and the results agree well with those obtained by other researchers.     

A FAMILY OF SPATIO-TEMPORAL LOCATION ANALYSIS PROBLEMS OF MOBILE TRADING

ABSTRACT It is well known that central place theory explains the spatial organization of permanent service centers in geographic space. But so far there has not been a theory or a set of models that can be used to fully explain the spatio-temporal organization of periodic service centers such as periodic marketplaces. This is notable because many scholars from geography, anthropology, and operations research have been trying to establish adequate models for explaining the spatio-temporal organization of periodic marketplaces during the past 50 years This article first introduces a family of eight classes of spatio-temporal location analysis problems related to a particular form of periodic marketing—mobile trading. It then presents a game theory model of two competing mobile traders as well as simulations on the synchronization of periodic marketplaces. Simulation results suggest that the synchronization of periodic marketplaces, resulting from the location patterns of two competing mobile traders, confirms the findings observed in empirical studies but does not follow those suggested by the consumer and the trader hypotheses. In addition, simulation results show that two competing traders agglomerate on a discrete linear structure.     

Higher order vibrations of thin periodic plates

A problem of higher order vibrations of thin periodic plates related to a plate periodicity is discussed. The applied model, based on the Kirchhoff plate theory assumptions and additional hypothesis of tolerance averaging [Wo?niak Cz, Wierzbicki E. Averaging techniques in thermomechanics of composite solids. Tolerance averaging versus homogenization. Poland, Cz?stochowa: Cz?stochowa University of Technology; 2000], makes it possible to take into account the effect of the periodicity cell size on the overall plate behaviour. Assuming more functions describing oscillations of the periodicity cell, we can investigate within the model not only fundamental vibrations but also higher order vibrations related to a periodic plate structure. These functions have to be properly chosen approximations of solutions to eigenvalue problem for natural vibrations of separated cell with periodic boundary conditions, [J?drysiak J. On vibrations of thin plates with one-dimensional periodic structure. Int J Eng Sci 2000;38:2023-2043]. Using the known two-dimensional plate models—the orthotropic plate model and finite element method as well as the discrete model, certain justifications of the proposed model are made.     

Entropy‐Based Optimal Sensor Placement for Model Identification of Periodic Structures Endowed with Bolted Joints

The number of sensors and the corresponding locations are very important for the information content obtained from the measured data, which is a recognized challenging problem for large‐scale structural systems. This article pays special attention to the sensor placement issues on a large‐scale periodically articulated structure representing typical pipelines to extract the most information from measured data for the purpose of model identification. The minimal model parameter estimation uncertainties quantified by the information entropy (IE) measure is taken as the optimality criterion for sensors placement. By utilizing the inherent periodicity property of this type of structure together with the Bloch theorem, a novel tailor‐made modeling approach is proposed and the computational cost required for dynamic analysis to form the IE with respect to the entire periodic structure can be dramatically reduced regardless of the number of contained periodic units. In addition, to avoid the error of dynamic modeling induced by conventional finite element method based on static shape function, the spectral element method, a highly accurate dynamic modeling method, is employed for modeling the periodic unit. Moreover, a novel discrete optimization method is developed, which is very efficient in terms of the number of function evaluations. The proposed methodology is demonstrated by both numerical and laboratory experiments conducted for a bolt‐connected periodic beam model.