白噪声参激一类余维二分岔系统矩Lyapunov指数

研究了白噪声参激一类三维中心流型上余维二分叉系统的矩Lyapunov指数.通过使用Arnold L摄动方法,Wedig W的线性随机变换法和Fourier级数展开方法,将系统的矩Lyapunov指数展开为小参数的幂级数,然后应用Fourier级数产生了矩Lyapunov指数展开式中第一项的特征值问题,并且在数值上验证了这些特征值序列是收敛的.     

斜拉索在轴向白噪声随机激励下的响应

建立了在考虑垂度以及拉索张力沿索长变化时拉索的参激随机微分方程,给出了在白噪声随机激励下预测拉索响应的近似理论解--用统计矩截断法求解矩方程,获得高斯闭合解和一阶非高斯闭合解.并采用数值模拟方法进行验证.随后以南京长江二桥A20拉索为研究对象,采用MonteCarlo数值方法对近似理论解进行验证.最后分析了白噪声激励强度、拉索阻尼及拉索张力对响应的影响.结果表明,斜拉索在零均值随机位移激励下的响应为非零均值;在高斯白噪声激励下的一阶位移响应随激励强度的增大而增大.随拉索阻尼和张力增大而减小.     

二阶随机参激系统的Lyapunov指数和稳定性

研究了二阶系统在随机噪声激励下的主共振响应和稳定性问题，用多尺度法确定了系统响应的幅值和相位角所满足的方程，讨论了系统的阻尼项、随机项等对系统响应的影响，求出了系统的不变测度和最大Lyapunov指数的解析表达式，由最大Lyapunov指数可得系统几乎必然稳定的充分必要条件。     

具有混合时滞的随机反应扩散神经网络指数稳定性

当电子在一个非均匀的电磁场中运动时,扩散现象不可避免的存在,因此在研究神经网络动态性能时还需要考虑状态空间随时间的变化.本文研究了一类具有混合时滞的随机反应扩散模糊细胞神经网络p阶矩指数稳定性问题.通过构造恰当的Lyapunov泛函并利用一些不等式分析技巧,得到了依赖于扩散系数的p阶矩指数稳定性充分条件.分析所得结果可发现较大的扩散系数更有利于系统实现稳定.     

窄带随机噪声参激作用下强非线性系统的响应

将改进的L-P(ModifiedLindstedt-Poincare)方法和随机多尺度法结合起来,研究了窄带随机噪声参激作用下强非线性VanderPol-Duffing系统的响应、稳定性和分叉问题。文中首先由改进的L-P方法引入变换参数,然后用多尺度法分离了系统的快变量,求出了最大Lyapunov指数的解析表达式,得到了系统几乎必然稳定的充分必要条件,讨论了系统的参数对稳定性的影响,分析了系统在1/2亚谐共振区的性态。理论分析与数值计算表明:在一定条件下系统将发生随机跳跃,且随着随机激励带宽的增大,扩散的极限环的宽度将逐渐增大。数值模拟结果表明:MLP方法结合随机多尺度法研究强非线性随机系统的响应、稳定性和分叉问题是有效的。     

有界噪声激励下典型非线性系统响应的最大Lyapunov指数估计

讨论有界噪声激励对一类典型非线性系统的动力学行为的影响。通过Monte-Carlo和小数据量方法,给出Holmes型杜芬振子在受周期激励和有界噪声激励作用下的样本响应及其最大Lyapunov指数结果。分析表明,在系统有确定性激励作用的导向时,可以由最大Lyapunov指数来判断系统运动是否混沌,且可得出推断：随机激励可诱发混沌亦可抑制混沌。然而,在系统仅受有界噪声激励时,难以从响应曲线和最大Lyapunov指数结果来判别系统的运动是否是混沌的。     

非高斯噪声激励下非线性漂移Fokker-Planck方程的非稳态解及其应用

非高斯噪声广泛存在于各种非线性系统，对非高斯噪声所驱动系统的非稳态演化行为进行研究可以更为深入的了解其内在的演化机理．本文对非高斯噪声和高斯白噪声共同驱动的非线性动力学系统的非稳态演化问题进行研究．首先应用格林函数的 $\Omega$ 展开理论在初始区域对非线性动力学系统进行线性化，然后结合本征值和本征矢理论推导出了该系统 Fokker-Planck 方程的近似非稳态解的表达式，最后以 Logistic 系统模型为例分析了非高斯噪声强度，关联时间及非高斯噪声偏离参数对非稳态解以及一阶矩的影响．研究结果表明，用 Logistic 模型描述产品产量增长时，其非稳态解可更好地反映产品产量在不稳定点附近的演化行为．     

黏弹性系统随机响应分析

应用等效非线性化方法分析了高斯白噪声激励作用下强非线性黏弹性系统随机响应。首先,通过广义谐和变换,黏弹性作用力可近似等效为拟线性阻尼和拟线性刚度两部分,进而原系统简化为无黏弹性项的非线性随机系统。其次,选取一类具有待定参数的等效非线性系统类。该等效非线性系统类具有精确稳态解,且和简化后的非线性随机系统具有相同的特性。然后,根据简化系统和等效非线性系统类之差的均方值最小原则,最终确定等效非线性系统类中的待定参数。最后以该系统的精确稳态随机响应近似表示原系统的随机响应。本文所提方法得到的解析结果与蒙特卡洛模拟方法得到的结果符合较好,证实了该方法的正确性。     

非高斯噪声和正弦周期力激励的阻尼谐振子系统的信息熵

阻尼谐振子广泛应用于固体理论、量子场论、量子力学和量子光学等不同的研究领域．信息熵在研究随机系统的动力学特性方面扮演着非常重要的角色．本文对非高斯噪声和正弦周期力激励的阻尼谐振子系统的信息熵变化率进行研究．首先通过路径积分近似,把非高斯噪声近似转化为高斯色噪声,得到了系统的Fokker-Planck方程,然后利用线性变换的方法简化了系统的Fokker-Planck方程,并结合Shannon信息熵的定义和Schwartz不等式原理得出了阻尼谐振子系统的信息熵变化率上界的表达式,最后分析了非高斯噪声和系统各参数对熵变化率上界的影响．     

结构在水平与竖向随机地震同时作用下的相关函数和谱密度

对单自由度结构在水平与竖向地震同时作用下的随机稳定性、响应及其相关函数和谱密度函数进行系统研究。首先利用Stratonovich和It随机微分方程与响应矩微分方程的互相关转化关系,建立了结构响应矩方程;然后根据Hurwitz随机稳定准则,获得了结构一阶和二阶响应矩渐近稳定的解析判别式;继而,利用复模态法获得了结构响应二阶矩的解析瞬态解和平稳解;最后利用It随机微分方程解具有的非可料函数性质,获得了结构位移、速度响应的自相关函数、互相关函数以及谱密度函数、互谱密度函数的解析解,给出了算例,并综合分析了各种参数对结构响应、稳定性以及相关函数和谱密度函数的影响。     

Stress analysis of a strip with a step and a crack

Stress analysis for a strip of which widths are different at the right and left handsides is carried out for before and after occurrence of a crack at a corner of a step. The strip is analyzed as a thin plate bending problem subject to transverse bending and torsion, and as a plane eleastic problem subject to bending in the plane and uniaxial tension. The rational mapping function of a sum of fractional expressions and complex variable method are used. Stress distribution and stress intensity factors are obtained.     

Calculation of a transient in a two-pole network with a thermistor

An analytical expression is derived which describes the variation of the thermistor temperature during a relay-effect transient process following an instantaneous change in the supply voltage in an R — R_T two-pole network.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 3, pp. 465–472, March, 1980.     

Interaction between a liquid and a cylindrical body touching a wall

An exact solution is obtained for the problem of interaction between the ideal liquid homogeneously moving at infinity and streamlining a round cylinder touching a solid wall.     

Imaging a point to a line with a single spherical mirror

Methods for imaging a single point source to a line image are discussed, and a design study of single spherical mirror systems that form aberration-free line images is presented. An expression forthe ray density along the line image is derived for such systems in the cases of (i) uniform beam profiles and (ii) Gaussian beam profiles. The resulting ray density profiles are illustrated for single spherical mirror systems over a wide range of design parameters.     

Influence lines for bending under a ring load of a free shell,a shell embedded in a soft medium and a shell containing a soft core

Summary Theoretical expressions for stresses and displacements have been derived for bending under a ring load of a free shell, a shell embedded in a soft medium, and a shell containing a soft core. Numerical work has been done for typical cases with anElliot 803 Digital Computer and influence lines are drawn therefrom.

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Einflußlinien für die Biegung einer freien Schale, einer Schale in einer weichen Bettung und einer Schale mit weichem Kern

Zusammenfassung Für die Biegung einer freien Schale, einer weich gebetteten Schale und einer Schale mit weichem Kern unter einer Ringlast werden Ausdrücke für die Spannungen und Verschiebungen hergeleitet. Die Ergebnisse wurden für einige typische Fälle mit einem DigitalrechnerElliot 803 numerisch ausgewertet. Die sich ergebenden Einflußlinien wurden graphisch dargestellt.

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Nomenclature A (),B () Functions of - a, t Mean radius and thickness of the shell - E _S , _S Young's modulus andPoisson's ratio of the shell - G _c , _c Shear modulus andPoisson's ratio of the casting or core - I ₀ (r),I ₁ (r) ModifiedBessel functions of the first kind and order zero and one respectively - K ₀ (r),K ₁ (r) ModifiedBessel functions of the second kind and order zero and one respectively - p Ring load, lb/in - U, W Displacement components in the casing or core in thez andr direction - u, w Displacement components of a middle surface point in the shell - _r , _rz Radial and shearing stress components - Independent variable of infinite integrals - k [3(1–S ²)a ²/t ²]^1/4 With 13 Figures     

Analysis of a Premature Failure of a Hub from a Diesel Generator of a High-Speed Motor Ship

Failure analysis is carried out on a fractured hub obtained from a diesel generator of a high-speed motor ship. Macrofractography, microfractography, standard optical metallography, material characterization techniques, and numerical modeling were used to verify the findings of the current investigation. Cracking initiation is attributed to fretting fatigue caused by a modification performed in the vicinity of the fractured hub. Operational vibrations contributed to the propagation of the cracks as typical fatigue cracks until final fracture.     

Piercing a metallic barrier with a jet of a dilute polymer solution

Results are shown pertaining to the action of jets of dilute polymer solutions on solid barriers. The piercing of a barrier is explained by the viscoelastic properties of aggregates which, during an impact, behave like solid particles.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 6, pp. 1090–1094, December, 1973.     

Interaction between a cylindrical shell in a fluid and a pulsating bubble

The dynamic behavior of a cylindrical fluid-immersed shell in a pressure wave initiated by a pulsating vapor-gas bubble that develops as a result of the action of laser radiation on the absorbing medium (metal) is examined experimentally and theoretically. The results of the experiments suggest that the amplitude of the shock wave that develops as a result of complete or partial vaporization of the absorbing medium is appreciably smaller than the amplitude of the waves due to pulsations of the bubble that is formed. Experimental data on the pattern of structural deformation are confirmed by calculations. The effect of load simulation on the behavior of the shell is established according to computational data.Translated from Problemy Prochnosti, No. 6, pp. 116–120, June, 1990.