共查询到20条相似文献，搜索用时 31 毫秒
1.
Winkler地基上四边自由矩形薄板的1/3次亚谐共振与混沌分析 总被引：1，自引：0，他引：1
研究Winkler地基上四边自由矩形薄板的复杂运动,按照弹性力学理论建立Winkler地基上四边自由受简谐激励作用矩形薄板的动力学方程;利用Galerkin方法将其转化为非线性振动方程;应用非线性振动的多尺度法求得了系统满足1/3次亚谐共振情况时的一次近似解,并进行数值计算;分析激励、调谐值、阻尼等对系统响应曲线的影响;应用Floquet理论分析了系统的稳定性问题;应用Melnikov方法得到了系统可能产生混沌运动的条件。 相似文献
2.
给出了横向磁场作用下矩形薄板的磁弹性振动方程,针对一边固定、三边简支的矩形薄板,通过位移模态展开,并利用Galerkin法得到两自由度内共振非线性振动微分方程组。算例分析中,利用数值方法得到了系统内共振时两阶模态的时间历程响应图和相平面图,并分别讨论了系统初值及磁场强度对系统振动的影响。结果表明,系统呈现明显的非线性内共振特征。 相似文献
3.
Stochastic Bifurcation of Rectangular Thin Plate Vibration System Subjected to Axial Inplane Gaussian White Noise Excitation 总被引：1，自引：1，他引：0
A stochastic nonlinear dynamical model is proposed to describe the vibration of rectangular thin plate under axial inplane excitation considering the influence of random environment factors. Firstly, the model is simplified by applying the stochastic averaging method of quasi-nonintegrable Hamilton system. Secondly, the methods of Lyapunov exponent and boundary classification associated with diffusion process are utilized to analyze the stochastic stability of the trivial solution of the system. Thirdly, the stochastic Hopf bifurcation of the vibration model is explored according to the qualitative changes in stationary probability density of system response, showing that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simple way on the potential applications of stochastic stability and bifurcation analysis. 相似文献
4.
The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed. 相似文献
5.
建立了具有摩擦支承边界的矩形薄板在面内载荷作用下的动力学方程 ,利用L S方法和奇异性理论对系统进行了局部分叉研究 ,讨论了非退化情况下Z2 分叉问题 .利用数值模拟给出了开折参数局部分叉集图和分叉响应曲线及物理参数平面上的分叉响应规律 ,其结果与解析和实验研究有很好的一致性 . 相似文献
6.
本文建立了一类两自由度变碰撞面的碰撞振动系统动力学模型,获得了系统的周期响应,推导出系统n-1周期运动的四维Poincaré映射。利用Poincaré映射方法,对系统单碰撞周期运动的稳定性与分岔进行分析,分析了系统n-1周期运动的Hopf分岔、周期倍化分岔及强共振情况下的亚谐分岔,研究了当分岔参数变化时碰撞振动系统由概周期碰撞运动向混沌运动的演化过程,为冲击振动系统的优化设计提供了理论依据。 相似文献
7.
针对机组轴系由电磁作用激发的振动问题,应用奇异性理论进行稳定性分析。首先求得转迁集,进而计算由转迁集而划分出的不同区域内的曲线形状,并分析这些曲线的稳定性,最后给出总的分岔图。所得结论对水电机组的电磁参数设计有一定的帮助作用。 相似文献
8.
为了研究温度场中非线性地基上矩形薄板受简谐激励的1/3次亚谐共振问题,应用弹性力学理论建立其动力学方程,应用Galerkin方法将其转化为非线性振动方程。利用非线性振动的多尺度分析方法求得系统1/3次亚谐共振的近似解,并进行数值计算。分析温度、地基系数、阻尼、几何参数、激励等对系统3次超谐共振的影响。得到了随参数变化响应曲线的变化规律。 相似文献
9.
A rectangular thin plate vibration model subjected to inplane stochastic excitation is simplified to a quasinonintegrable Hamiltonian system with two degrees of freedom. Subsequently a one-dimensional Ito? stochastic differential equation for the system is obtained by applying the stochastic averaging method for quasi-nonintegrable Hamiltonian systems. The conditional reliability function and conditional probability density are both gained by solving the backward Kolmogorov equation numerically. Finally, a stochastic optimal control model is proposed and solved. The numerical results show the effectiveness of this method. 相似文献
10.
11.
Translational torsional coupled model based nonlinear dynamic analysis of an NGW planetary gear train 总被引：1，自引：0，他引：1
This paper aims to investigate the nonlinear dynamic behaviors of an NGW planetary gear train with multi-clearances and manufacturing/assembling errors. For this purpose, an analytical translational ? torsional coupled dynamic model is developed considering the effects of time-varying stiffness, gear backlashes and component errors. Based on the proposed model, the nonlinear differential equations of motion are derived and solved iteratively by the Runge-Kutta method. An NGW planetary gear reducer with three planets is taken as an example to analyze the effects of nonlinear factors. The results indicate that the backlashes induce complicated nonlinear dynamic behaviors in the gear train. With the increment of the backlashes, the gear system has experienced periodic responses, quasi-periodic response and chaos responses in sequence. When the planetary gear system is in a chaotic motion state, the vibration amplitude increases sharply, causing severe vibration and noise. The present study provides a fundamental basis for design and parameter optimization of NGW planetary gear trains. 相似文献
12.
变厚度矩形薄板弯曲问题的DQ法研究 总被引：1，自引：0，他引：1
针对矩形薄板的线性挠曲控制微分方程及其边界条件,在空间域采用DQ法离散,得到以板各节点弯曲挠度为全部待定参数的线性方程组,只需一次求解该方程组即得到各节点的弯曲挠度,再由高阶Lagrange插值得到薄板全域内的任意点挠度。 相似文献
13.
基于麦克斯威尔方程,给出导电薄板的非线性磁弹性振动方程,以及磁场环境下的电动力学方程和电磁力表达式。在此基础上,应用伽辽金法导出相应的非线性振动微分方程组,研究横向恒定磁场中周期载荷作用下梁式薄板的稳定性问题。根据李雅普诺夫近似稳定性理论,对稳态解的稳定性进行分析,得到稳定性的判定条件。通过对算例特征值的求解对振动的稳定性进行分析。 相似文献
14.
The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional
elasticity. Noticing many FGMs may have temperature-dependent properties, the material constants were further considered as
functions of temperature. A solution method based on state-space formulations with a laminate approximate model was proposed.
For a thin plate, the method was clarified by comparison with the thin plate theory. The influences of material inhomogeneity
and temperature-dependent characteristics were finally discussed, through numerical examples.
Project (No. 10002016) supported by National Natural Science Foundation of China 相似文献
15.
《天津大学学报(英文版)》2015,(4)
The stability and local bifurcation of the lateral parameter-excited resonance of pipes induced by the pulsating fluid velocity and thermal load are studied. A mathematical model for a simply supported pipe is developed according to Hamilton principle. The Galerkin method is adopted to discretize the partial differential equations to the ordinary differential equations. The method of multiple scales and the singularity theory are utilized to analyze the stability and bifurcation of the trivial and non-trivial solutions. The transition sets and bifurcation diagrams are obtained both in the unfolding parameter space and physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and verify the stability and local bifurcation analyses. The critical thermal rates are obtained both by the numerical simulation and the local bifurcation analysis. The natural frequency of lateral vibration decreases as the mean fluid velocity or the thermal rate increases according to the numerical results. The present work can provide valuable information for the design of the pipeline and controllers to prevent structural instability. 相似文献
16.
ＩＮＴＲＯＤＵＣＴＩＯＮＡｓｋｎｏｗｎ ,ｔｈｅｒｍａｌｂｅｈａｖｉｏｒｓｏｆｓｔｒｕｃｔｕｒｅｓｍｕｓｔｂｅｃｏｎｓｉｄｅｒｅｄｉｎｍａｎｙｓｉｔｕａｔｉｏｎｓ.Ｓｔｕｄｙｏｆｔｈｅｒｍａｌｅｆｆｅｃｔｏｎｄｅｆｏｒｍａｔｉｏｎｓａｎｄｓｔｒｅｓｓｅｓｏｆ 相似文献
17.
王立明 《廊坊师范学院学报(自然科学版)》2009,9(4):56-59
对“旋转单摆”的运动进行研究,建立系统的动力学方程,用线性稳定性分析方法讨论平衡点附近邻域的稳定性,给出了系统静态分岔图和运动的相图,利用Jacobi椭圆函数得出不同转速下系统作周期运动的解析解,并绘出图形加以说明。 相似文献
18.
本文介绍了研究振动方程时的几种分析方法,并讨论了方程解的物理意义。自然界中最基本的振动是简谐振动,讨论简谐振动是研究复杂振动现象的基础,对其研究和分析方法很多,本文介绍几种求解振动方程的几种分析方法：1.常系数线性微分方程的一般求解法;2.拉普拉斯逆变换法;3.简谐振动的矩阵求解法,并讨论了方程解的物理意义。 相似文献
19.
Xu Xu Shan Feng 《上海大学学报(英文版)》1998,2(2):112-116
１ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｌａｓｓｉｃａｌｔｈｉｎｐｌａｔｅｔｈｅｏｒｙｏｆｖｉｂｒａｔｉｏｎｉｓｂａｓｅｄｏｎｔｈｅＫｉｒｃｈｈｏｆｈｙｏｔｈｅｓｉｓ,ａｎｄｔｈｅｅｆｅｃｔｏｆｔｒａｎｓｖｅｒｓａｌｓｈｅａｒｄｅｆｏｒｍａｔｉｏｎａｎｄｒ... 相似文献
20.
一类反应扩散方程的分歧分析 总被引：2，自引：2，他引：0
王华涛 《内江师范学院学报》2009,24(12):20-23
讨论了一类反应扩散方程的分歧（分岔）现象．运用一般线性全连续场谱定理和L—S（李雅普诺夫-施密特）约化方法得到了此方程的一阶近似形式并求出了从平凡解分歧出的非平凡解的具体表达式．最后运用一些经典分歧定理得到了一些重要的分歧结果,给出了分歧图形． 相似文献