变曲率平面拱的自由振动分析

发布时间：2018-01-10 19:14

  本文关键词：变曲率平面拱的自由振动分析　出处：《兰州理工大学学报》2017年02期 　论文类型：期刊论文

  更多相关文章： 变曲率 平面拱 自由振动 频率 传递矩阵法(TMM)

【摘要】：基于Euler-Bernoulli梁理论和传递矩阵法(TMM),研究变曲率平面拱的自由振动问题.考虑拱轴线的曲率沿张角呈线性变化,将变曲率平面拱在弧线方向离散成多个曲拱单元,用TMM推导单元传递矩阵和变曲率平面拱的自由振动特征方程.求解不同边界条件下变曲率平面拱自由振动的固有频率,考虑曲率变化系数对于拱的自由振动频率的影响,将求得的两端固定圆弧拱的结果与现有文献作了比较,证明TMM对求解该问题的有效性.结果表明,当拱轴线的曲率沿张角呈线性变化,不同边界条件下变曲率平面拱各阶自由振动频率随曲率变化系数的增大而增大,且相同曲率变化系数增幅下随自由振动频率阶数的提高,自由振动频率的增幅也在加大.
[Abstract]:Euler-Bernoulli beam theory and transfer matrix method (TMM), based on the study of free vibration problem of curvature plane arch. Considering the curvature of the arch axis along the angle changes linearly, the variable curvature plane arch in the arc direction into a plurality of discrete arch unit, free vibration characteristic equation of transfer matrix with TMM derived unit and variable curvature plane arch. The natural frequency of variable curvature arch plane free vibration solution under different boundary conditions, considering the effect of curvature coefficient for free vibration frequency of the arch, the arch will be fixed at both ends of the arc of the results are compared with the existing literature, prove the effectiveness of TMM to solve the problem. The results show that when the curvature of the arch axis along the angle changes linearly, the variable curvature arch plane of each order free vibration frequency increases with the curvature coefficient under different boundary conditions, and the same curvature coefficient increase with free vibration The increase in the frequency of the dynamic frequency increases the frequency of the free vibration.

【作者单位】： 兰州理工大学理学院;
【基金】：甘肃省自然科学基金(148RJZA017)
【分类号】：O32
【正文快照】： 拱作为一种常见的结构形式,在土木、航空和机械工程等领域得到广泛的应用,因此对其静、动力学行为的研究有着十分重要的意义,特别对拱或曲梁的自由振动问题,很多学者都进行了大量的研究.例如,Karnovsky[1]对各种类型均匀材料拱结构的强度、稳定性和振动问题求解的基本方法和过，

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