二次非线性粘弹性圆板的2/1⊕3/1超谐解

计及材料的非线性弹性和粘性性质 ,研究了圆板在简谐载荷作用下的 21 31超谐解 ,导出了相应的非线性动力方程。提出一类强非线性动力系统的叠加 叠代谐波平衡法。将描述动力系统的二阶常微分方程 ,化为基本解为未知函数的基本微分方程 ;及分岔解为未知函数的增量微分方程。通过叠加 迭代谐波平衡法得出了圆板的 21 31超谐解。对叠加迭代谐波平衡法和数值积分法进行了比较 ,两者结果吻合很好。并且讨论了 21 31超谐解的渐近稳定性     

具脱层的轴对称层合圆板的非线性振动分析

基于Von Karman板理论,应用三分区模型,建立了考虑横向剪切效应时具任意脱层的正交对称铺设轴对称层合圆板在径向压力荷载作用下的非线性运动微分方程。对未知变量在空间上采用Bessel函数,应用Galerkin法,得到无量纲的仅关于时间函数的运动微分方程,并应用谐波平衡法对此方程进行求解,算例中讨论了不同脱层半径、脱层深度对具脱层的正交对称铺设轴对称层合圆板非线性幅频响应的影响。     

非线性动力系统的频率近似法

给出非线性动力系统周期振动的频率近似法，本法将描述动力系统的非线性微分方程，化为以相角为自变量，振动频率为未知函数的积分方程，将弹性恢复力表示为线性及非线性两部分，从而得到积分方程的近似解，即频率的近似表达式。     

强非线性动力系统的频率增量法

提出一类强非线性动力系统的暧时频率增量法,将描述动力系统的二阶常微分方程,化为以相位为自变量、瞬廛频率为未知函数的积分方程;用谐波平衡原理,将求解瞬时频率的积分问题,归结为求解以频率增量的Fourier系数为独立变量的线性代数方程组;给出了若干例子。     

非线性时滞反馈控制系统超谐共振分析

采用增量谐波平衡法求解了非线性时滞微分方程的超谐共振解,研究了时滞、反馈控制增益、激励幅值、非线性项系数等系统参数对系统超谐共振响应的影响,分析了超谐共振响应随系统参数变化的规律。结果表明:三次谐波与一次谐波振幅的比值随时滞量呈周期性变化;反馈控制增益对系统超谐共振的影响与非线性项系数和激励幅值有关;随着非线性项系数和激励幅值的不断增大,三次谐波项与一次谐波项振幅的比值都是先增大后减小,而且减小的趋势逐渐减弱;一次谐波成份在振幅中占主导地位。     

强非线性振动系统周期解的能量迭代法

对于完全强非线性系统：x^.. g(x) f(x,x^.)x^.=0,提出求周期近似解析解以及这些解的稳定性的新方法。式中，g(x)、f(x,x^.)x^.分别是x,x、x^.的非线性函数。方法是基于能量原理，求出其一次近似解析解，然后引进牛顿迭代思想，得到周期系统数微分方程，最后根据谐波平衡原理及最小二乘法求其高次近似解，高次近似解的表达式由计算机辅助推导。计算参考文献[2]和[3]中的例题，令其中ε=1，研究该完全强非线性系统的周期解及其稳定性，本文方法与龙格-库塔数值法算得的结果对照如图1-3所示，它们表明本文方法不仅有效而且精度较高。     

静载荷对夹层圆板超谐波共振的影响

研究静载荷作用下夹层圆板的超谐波共振问题．基于Hoff型夹层板理论,给出了静载荷作用下夹层圆板的非线性动力学方程．应用Galerkin法推导了静载荷作用下夹层圆板的轴对称非线性振动方程．运用多尺度法分别对系统的三次超谐波问题和二次超谐波问题进行了求解,并依据Lyapunov稳定性理论得到了系统稳态运动的稳定性判据．通过算例,得到了周边简支约束下夹层圆板三次超谐波共振和二次超谐波共振的幅频响应曲线图、振幅-静载荷响应曲线图、振幅-激励力幅值响应曲线图;研究了不同参数对系统振幅的影响规律,并对解的稳定性进行了分析．     

圆板在物体撞击下的非线性动力响应

本文在Von Kármán大位移的意义上,利用虚位移原理伽辽金方法建立了圆板在物体撞击下的非线性动力响应的控制微分方程,在研究响应问题时,考虑了冲击载荷与圆板位移响应之间的耦合影响,文中使用时间增量法和奇异摄动理论求解问题的控制方程,获得了固支圆板非线性动力响应的近似解,并且求解了具体算例,绘出了圆板位移、应力响应曲线以及冲击力随时间的变化曲线。     

变厚度圆板的非线性强迫振动

本文研究了厚度呈幂指数规律变化的变厚度圆饭的非线性强迫振动问题。文中首先用半解析法求解了动态Von Ka＇rma＇n大变形方程,导出了周期均布荷载作用下轴对称变厚度薄圆板的非线性强迫振动微分方程。然后用小参数摄动法求解了振动方程,得到了非线性的非共振周期解和共振周期解。绘制了振幅——频率关系图。     

计算圆板大振幅非线性振动频率的平均刚度法

本文用平均刚度法研究圆板大振幅非线性振动的频率问题，导出了相应的非线性广义特征值方程，构造了一种避免发散并能加速收敛的加权平均迭代法，计算结果与Ｋａｎｔｏｒｏｖｉｃｈ时间平均法的解十分吻合。     

Galileo E1/E5/E6数字中频信号仿真

新伽利略系统计划提供E1、E5和E6导航信号服务于民用导航、商业服务和生命安全服务领域,预计导航性能将大幅提升.本文旨在设计一种基于软件的伽利略E1/E5/E6中频信号发生器以模拟未来的伽利略导航系统.首先简要概述了伽利略信号及其在无线电频段的分布,包括E1、E5和E6信号的信号结构和特点.然后对仿真系统的组成进行了详细描述并通过Matlab软件进行仿真,重点分析了所有导航信号的功率谱密度(PSD).结果表明该仿真系统可为伽利略接收机的设计和测试提供可控信号源.     

Analysis of 1:1 internal resonance of a CFRP cable with an external 1/3 subharmonic resonance

Nonlinear Dynamics - Based on the non-planar vibration equations of a cable made of carbon fiber reinforced polymer (CFRP), the nonlinear behaviors of the cable are studied. The one-to-one internal...     

1/3 subharmonic solution of elliptical sandwich plates

IntroductionInrecentyears,withtheessentialadvantageoflightweightandhighrigidity ,sandwichplatesandshellshavebeenusedasanimportantpatternofstructuralelementsinaeronautical,astronauticalandnavalengineering .However,nonlinearproblemsforsandwichplatesandshellsareonlyinvestigatedbyafewbecauseofthedifficultiesofnonlinearmathematicalproblems.LiuRen_huaiandXuJia_chu[1,2 ]andothershavemadesomeinvestigationsinthisfield .Bifurcationofnonlinearvibrationforsandwichplateshasnotyetbeeninvestigated .Inthisp…     

Validation of 1D model for methane/air/Pt combustion in stagnation flow

A 2D model is built on the package of FLUENT to study the effects of radial aspect ratio (R/W), length-to-width ratio (L/W), strain rate (S _R), and buoyancy (Ri=Gr/Re ²) on the validation of the simplified 1D model. In the present 2D model, the methane/air homogeneous reaction mechanism of Peters and the methane/air/platinum heterogeneous reaction mechanism of Deutschmann are applied. By comparison between the 1D and 2D numerical results, it is found that the validation of 1D model is highly related with the catalytic stagnation reactor configuration. For length-to-width ratio L/W = 1 configuration, 1D laminar model is applicable when the radial aspect ratio R/W > 0.4. For R/W = 0.6, the reactor exhibited 1D characteristics when L/W < 1. Compared with the temperature and species profiles, the velocity distribution along the axis is more sensitive to the change of radial aspect ratio and length-to-width ratio. With increasing of the strain rate, the flame front goes closer to the catalytic wall surface and the difference between the 1D and 2D results decreases. For a valid 1D simulation, it is recommended that the strain rate should be greater than 20 s^-1. The effects of natural convection can be neglected when Ri < 5.     

The Parametrically Forced Pendulum: A Case Study in 1 1/2 Degree of Freedom

This paper is concerned with the global coherent (i.e., non-chaotic) dynamics of the parametrically forced pendulum. The system is studied in a === degree of freedom Hamiltonian setting with two parameters, where a spatio-temporal symmetry is taken into account. Our explorations are restricted to large regions of coherent dynamics in phase space and parameter plane. At any given parameter point we restrict to a bounded subset of phase space, using KAM theory to exclude an infinitely large region with rather trivial dynamics. In the absence of forcing the system is integrable. Analytical and numerical methods are used to study the dynamics in a parameter region away from integrability, where the analytic results of a perturbation analysis of the nearly integrable case are used as a starting point. We organize the dynamics by dividing the parameter plane in fundamental domains, guided by the linearized system at the upper and lower equilibria. Away from integrability some features of the nearly integrable coherent dynamics persist, while new bifurcations arise. On the other hand, the chaotic region increases.2000 Mathematical Subject Classification: 37J20, 37J40, 37M20, 70H08.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.