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characteristics of evolution
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  演化特征
    The characteristics of evolution and prediction method for side slope have been studied with the fractal geometry,the related dimension reflecting the dynamic characters of side slopes was found.
    本文应用分形几何理论研究了边坡的演化特征和预测方法,寻求了反映边坡系统动态特性的关联维。
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    The investigation shows that the probability density curves of the stochastic structural response have the characteristics of evolution, and they are far from normal distribution, at some time they even have double peaks.
    研究表明,随机结构反应的概率密度具有演化特征,且概率密度曲线与正态分布差异甚大,甚至可能出现双峰曲线。
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  characteristics of evolution
Furthermore, the characteristics of evolution for the disturbances of different modes in the hypersonic sharp cone boundary layer were discussed.
      
Changes in the quantitative characteristics of evolution of the phase variables (maximum Lyapunov exponent and Hausdorff dimension) are also studied as a function of the external field.
      


The characteristics of evolution and prediction method for side slope have been studied with the fractal geometry,the related dimension reflecting the dynamic characters of side slopes was found.The practical calculation and analysis show that the stability loss of side slope has a character of fractal dimension.Such fractal theory and fractal dimension offer a new way for side slope prediction.

本文应用分形几何理论研究了边坡的演化特征和预测方法,寻求了反映边坡系统动态特性的关联维。通过实例计算和分析,表明边坡变形失稳过程具有很好的分维特性,分形分维方法为边坡预测研究提供了新的途径。

Probability density evolution method for the analysis of stochastic structural dynamic response is presented. Based on the finite element method, the state equations of structural response containing random parameter are deduced. The probability density evolution equation (PDEE) of the stochastic structural response is then established by introducing augmented state vector. Combing the precise integration method with the Lax-Wendroff difference scheme will lead to numerical method for the PDEE. A case is studied...

Probability density evolution method for the analysis of stochastic structural dynamic response is presented. Based on the finite element method, the state equations of structural response containing random parameter are deduced. The probability density evolution equation (PDEE) of the stochastic structural response is then established by introducing augmented state vector. Combing the precise integration method with the Lax-Wendroff difference scheme will lead to numerical method for the PDEE. A case is studied on the response of an 8-storey floor-shear stochastic structure and the results are compared with that evaluated by the Monte Carlo method. The investigation shows that the probability density curves of the stochastic structural response have the characteristics of evolution, and they are far from normal distribution, at some time they even have double peaks.

提出了随机结构动力反应分析的概率密度演化方法。基于有限单元法基本原理,导出了含有随机参数的结构反应状态方程,进而,通过引入扩展状态向量,建立了随机结构反应的概率密度演化方程。将精细时程积分方法与Lax-Wendroff差分格式相结合,探讨了求解概率密度演化方程的数值方法。对一个8层层间剪切型随机结构进行了算例分析,并与Monte Carlo方法的结果进行了比较。研究表明,随机结构反应的概率密度具有演化特征,且概率密度曲线与正态分布差异甚大,甚至可能出现双峰曲线。

In the present paper, a method was put forward to evaluate the evolution probability of the node force for memory-less structure under displacement-controlling loading. In the method, the force and nonlinear configuration state were combined to form a force-state compound vector Markov process. According to the separated analysis method, the state transition rates of probability were obtained firstly and then the joint probability evolution equation of the force-state compound vector Markov process...

In the present paper, a method was put forward to evaluate the evolution probability of the node force for memory-less structure under displacement-controlling loading. In the method, the force and nonlinear configuration state were combined to form a force-state compound vector Markov process. According to the separated analysis method, the state transition rates of probability were obtained firstly and then the joint probability evolution equation of the force-state compound vector Markov process could be set up. By solving the joint equations, the probability characteristic of evolution of the nonlinear configuration state and the node force could be evaluated. Furthermore, it is of significance that the evolution e-quations of the nonlinear configuration states can be deduced directly from the force-state joint evolution equations whereas the force and state can not be uncoupled in the evolution equations of the force.

本文提出了位移加载机制下求解无记忆特性结构结点力的概率密度演化规律的方法。该方法将力与非线性构形状态演化联合起来,组成力-状态混合向量马氏过程。采用分离式分析方法进行状态转移概率速率分析,然后建立力-状态联合概率密度演化方程。求解这一方程可分别得到非线性构形状态演化和结点力随机演化的概率结构。意味深长的是,非线性构形状态的演化方程可以直接由力-状态联合演化方程推导出来,而力的概率演化方程则不能实现力与状态之间的解耦。

 
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