非线性粘弹性梁的混沌运动

The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.     

非线性粘弹性梁弯曲的失记效应

Based on the Leaderman constitutive relations in nonlinear viscoelasticity and the linear geometrical assumption, a mathematical model for the bending of nonlinear viscoelastic beams was established in this paper. The Laplace transformation method and the Titchmarsh theorem were used to prove that some relations exist between solutions to bending problems of visco- and elastic beams, which reveals the fugue effect of viscoelastic materials. The high-order Galerkin approximate solution to the quasi-static response of nonlinear viscoelastic beams under a step load was obtained by using the new method suggested in this paper as well as the Mathematica software and the Newton iteration technique.     

损伤粘弹性梁-柱的广义变分原理

从损伤的粘弹性材料的卷积型本构关系出发,建立了在小变形下损伤粘弹性梁-柱的控制方程,提出了以卷积形式表示的损伤粘弹性梁-柱弯曲问题的泛函,并给出了损伤粘弹性梁-柱的广义变分原理.应用这个广义变分原理,可分别给出梁-柱位移和损伤满足的基本方程,以及相应的初始条件和边界条件.     

材料和几何非线性粘弹性柱的动力学模型及其简化

建立了描述具有几何和物理非线性均匀柱动力学行为的偏微分－积分方程,柱的材料满足Ｌｅａｄｄｅｒ－ｍａｎ非线性本构关系,对两端简支的情形,采用Ｇａｌｅｒｋｉｎ方法简化为常微分一积分方程;然后通过引进附加变量的方法进一步简化为常微分方程。     

股票市场价格行为的非线性确定性动力学模型

1引论1．1效率市场理论的产生及其发展概况早在1900年,Bachelier［1］在他的数学博士论文中就提出了“效率市场”的理论思想。他描述了价格的随机行走模型（Randomwalk）,概率常扩散──也叫布朗运动和鞅,这些都是效率市场的数学表述。在1953年,当时一位颇有名的统计学家Kendall［2］发表了一篇有争议的文章,即“经济时间序列分析,第一部分：价格”。此文的初衷是想借助于问世不久的电子计算机,追寻出股票价格波动的模式。研究结果显示,股市价格没有任何模式可寻：它就像“一个醉汉走步一样,几乎宛如机会之魔每周扔出一个随机数…     

一类粘弹性动力学方程的通解

本文建立圆柱体任意两个截面间的一般粘弹性转动力学方程。由于此方程为变系数的二阶线性的非齐次常微分方程组,没有统一的求解方法。因此,我们针对其中的一类方程求得其通解。     

一类非线性复杂网络的混沌动力学行为研究

基于系统最大李雅普诺夫指数的数学计算方法,从网络本身的拓扑结构出发,给出了一类非线性复杂网络对初始状态敏感的充分条件,同时仿真出网络所有李雅普诺夫指数随着时间推移的变化趋势图以及系统状态的相轨迹图,成功实现了网络的混沌反控制。     

粘弹性开敞浅壳的动力学性质

On the basis of the Kármán-Donnell theory of thin shells with large deflections and the Boltzmann laws for linear viscoelastic materials, the mathematical model for viscoelastic open shallow shells was formulated. By using the Galerkin average method, the original integro-partial-differential dynamic system was simplified as a integro-ordinary-differential dynamic system, which can be transformed into a ordinary differential dynamic system by introducing new variables. The dynamical behavior was studied by some classical methods. Dynamical properties, such as, chaos, strange attractor, limit cycle etc., were discovered. Supported by the Development Foundation of Shanghai Municipal Commission of Education (99A01)     

轴向载荷作用下基桩非线性动力学行为探讨

综合利用数学、力学和桩基工程中的理论和方法来解决基桩非线性动力学分析中的主要问题．根据动力学原理建立在轴向载荷作用下基桩非线性动力学模型，综合应用多种数值方法进行理论分析、数值模拟和待定参数的研究，寻求适合基桩非线性动力学行为分析的有效方法，给出一些有益的结论．     

伽马能谱仪中开关功率变换器非线性动力学行为

为提高伽马能谱仪中开关功率变换器的工作稳定性,研究了开关功率变换器非线性行为的分析方法,其中包括数值仿真、理论分析和电路实验研究方法。以电压控制模式的Buck变换器为例,分析该变换器的工作过程,建立相应的数学模型,对该模型进行数值仿真,观察到该变换器的非线性行为。从理论上分析该现象的本质原因,通过电路实验来验证。最后,证明这3种方法对研究开关功率变换器非线性行为的可行性和准确性,为伽马能谱仪中开关功率变换器的设计提供理论指导。     

Dynamical Behavior of Nonlinear Viscoelastic Timoshenko Beams with Damage on a Viscoelastic Foundation

Based on convolution-type constitutive equations for linear viscoelastic materials with damage and the hypotheses of Timoshenko beams with large deflections, the nonlinear equations governing dynamical behavior of Timoshenko beams with damage on viscoelastic foundation were firstly derived. By using the Galerkin method in spatial domain, the nonlinear integro-partial differential equations were transformed into a set of integro-ordinary differential equations. The numerical methods in nonlinear dynamical systems, such as the phase-trajectory diagram, Poincare section and bifurcation figure, were used to solve the simplified systems of equations. It could be seen that simplified dynamical systems possess the plenty of nonlinear dynamical properties. The influence of load and material parameters on the dynamic behavior of nonlinear system were investigated in detail.     

Chaotic Motions of Nonlinear Viscoelastic Beams

l introductionThe Galerkin trUncation is widely used to stody thedynandcal behavior (especially the nonlinear dynamicalbehavior) of,trU.tUre,[i]. The Galerkin method is alsoaPPlied to stUdy dynamical behavior of viscoelashcbeams. Suire and Cederbaum [2] analyzed periodic andchaohc behavior of viscoelastic beams with the Idledeflection, and the constitUtive relation in their work isthe BoltZmann superposition Principle. Argyris[']myes-tigated chaohc motion of viscoelastic beamsbased on a …     

嵌岩桩非线性动力学特性

The nonlinear dynamic characteristics of a pile embedded in a rock were investigated. Suppose that both the materials of the pile and the soil around the pile obey nonlinear elastic and linear viscoelastic constitutive relations. The nonlinear partial differential equation governing the dynamic characteristics of the pile was first derived. The Galerkin method was used to simplify the equation and to obtain a nonlinear ordinary differential equation. The methods in nonlinear dynamics were employed to solve the simplified dynamical system, and the time-path curves, phase-trajectory diagrams, power spectrum, Poincare sections and bifurcation and chaos diagrams of the motion of the pile were obtained. The effects of parameters on the dynamic characteristics of the system were also considered in detail.     

冷弯薄壁型钢梁的滞回性能非线性有限元分析

在确定冷弯薄壁型简支钢梁应力-应变模型的基础上,采用有限元软件ANSYS对冷弯薄壁型简支钢梁荷载-位移关系进行非线性有限元计算分析。对冷弯薄壁型简支钢梁荷载-位移关系骨架线、弯矩-曲率关系骨架线进行比较分析,主要比较了跨高比、宽厚比对其的影响。     

压型钢板组合梁的有限元模型

利用ANSYS有限元软件对压型钢板组合梁模型进行了有限元数值模拟分析。将有限元分析结果与试验结果进行比较,验证了有限元模型的合理性。     

均布载荷作用下悬臂不可压饱和多孔梁的非线性变形

Nonlinear bending of cantilever incompressible poroelastic beams subjected to a uniform load is investigated with the constraint that fluid flow is only in the axial direction. The governing equations for large deflection of the poroelastic beam are derived from theory of incompressible saturated porous media. Then, nonlinear responses of a cantilever beam with impermeable fixed end and permeable free end are examined with the Galerkin truncation method. The deflections and bending moments of the poroelastie beam and the equivalent couples of the pore fluid pressures are shown in figures. The differences of the results between the large deflection and the small deflection theories are analyzed. It is shown that the results of the large deflection theory are smaller than those of the small deflection theory, and the time needed to approach their stationary states for the large deflection theory is shorter than that for the small deflection theory.     

Cubic Spline Solutions of Nonlinear Bending and Buckling of Circular Plates with Arbitrarily Variable Thickness

The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.     

Axisymmetrical Nonlinear Bending and Buckling of a Circular Plate Under Large Load

With the terms of the exact series solution taken as trial functions, the method of point collocation was used to calculate the large deflection of a circular plate. The axisymmetrical bending formulae were developed for the calculation of a circular plate subjected to polynomial distributed loads, a concentrated load at the center, uniform radial forces and moments along the edge or their combinations. The support may be elastic. The buckling load was calculated. Under action of uniformly distributed load, central load or their compound load, solutions were compared with those obtained by other methods, Buckling beyond critical thrust was compared with that calculated by the power series method. The method presented in this paper has advantages of wide convergent range, high precision and short computing time. Moreover, the computing time is nearly independent of the complexity of the loads.