集中周期激振力作用下深拱的面内动力稳定的研究

发布时间：2018-02-28 23:14

本文关键词： 深拱集中周期激振力动力稳定性 mathieu-hill方程动力不稳定域　出处：《广州大学》2015年硕士论文　论文类型：学位论文

【摘要】：随着现代科学技术的发展,结构日趋采用高强度材料和薄壁结构,越来越向轻薄大跨方向发展,结构稳定性问题日益突出,直接威胁到了人们的生命财产安全。本文采用理论分析、数值求解和模型试验相结合的方法,对拱顶受集中周期激振力作用的两端固结圆弧深拱的动力稳定性展开了以下研究:(1)推导了深拱的动力稳定方程。根据深拱结构的动力特征,抽象出其拱顶受集中周期激振力作用下的面内动力失稳力学图式,设定了相应的位移变形函数,且基于已有压弯深拱结构的静力弯曲微分方程式,引入惯性力,根据克希霍夫方程式理论推导出圆弧深拱的弯曲振动微分方程式,再采用Hamilton变分原理和伽辽金方法,推导了关于固结圆弧深拱的mathieu-hill方程;通过MATLAB编程求解mathieu-hill方程,获得了深拱面内动力稳定边界,绘制了结构动力不稳定区域分布图。(2)完成了深拱结构动力稳定模型激振试验。设计制作了不同矢跨比以及不同配重下深拱的试验模型,通过激振实验对深拱试验模型的动力失稳全过程进行测试分析,跟踪了动力失稳平衡路径和失稳的变形过程,揭示了竖向周期激振力下深拱动力失稳模态,验证了本文所求解的理论动力不稳定域的正确性,总结了动力失稳域与激振荷载频率间的关系。(3)进行了深拱结构动力失稳的参数分析。分析了深拱矢跨比、拱顶配重对其动力稳定性能的影响规律,研究结果表明:相同条件下,随着矢跨比的增加,结构发生参数共振的频率呈下降趋势,动力不稳定区域也随之变窄;同样,随着拱顶配重的增加,深拱结构发生参数共振的频率逐渐下降,动力不稳定区域也逐渐变窄;失跨比与配重均是影响结构失稳模态的重要因素;结构发生参数拱振的频率为外部激振力频率的2倍。
[Abstract]:With the development of modern science and technology, the structure adopts high strength material and thin wall structure day by day, and develops more and more in the direction of light, thin and long span. The problem of structural stability becomes more and more prominent. It is a direct threat to the safety of people's life and property. In this paper, the method of theoretical analysis, numerical solution and model test is used. In this paper, the dynamic stability of a deep arch with two end-to-end consolidation arc subjected to concentrated periodic excitation force is studied as follows: 1) the equation of dynamic stability of the deep arch is derived. According to the dynamic characteristics of the deep arch structure, The mechanical schema of in-plane dynamic instability of the arch under the action of concentrated periodic excitation force is abstracted, the corresponding displacement and deformation function is set up, and the inertia force is introduced based on the static bending differential equation of the existing deep arch structure. According to the Kirchhoff equation theory, the differential equation of bending vibration of deep arc arch is derived, and then the mathieu-hill equation about the deep arc arch is derived by using Hamilton variational principle and Galerkin method, and the mathieu-hill equation is solved by MATLAB programming. The dynamic stability boundary of deep arch plane is obtained and the regional distribution map of structural dynamic instability is drawn. The dynamic stability model excitation test of deep arch structure is completed. The test model of deep arch with different ratio of rise-span and different counterweight is designed and made. The whole process of dynamic instability of deep arch test model is tested and analyzed by exciting experiment. The dynamic instability equilibrium path and deformation process are followed, and the dynamic instability mode of deep arch under vertical periodic excitation force is revealed. The validity of the theoretical dynamic instability domain is verified, and the relationship between the dynamic instability region and the frequency of the excitation load is summarized. The parameter analysis of the dynamic instability of deep arch structure is carried out, and the ratio of the deep arch to the span is analyzed. The results show that the frequency of parametric resonance of the structure decreases with the increase of the rise-span ratio, and the dynamic instability region becomes narrower under the same conditions. With the increase of the weight of arch roof, the frequency of parametric resonance of deep arch structure decreases gradually, and the dynamic instability region becomes narrower, and the ratio of span loss and counterweight is an important factor affecting the instability mode of the structure. The frequency of arched vibration is twice as much as that of external excitation force.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U441;U443

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