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基于轴向受力梁的振动微分方程,提出同时考虑拉索垂度及抗弯刚度的拉索振动非线性微分方程,并引入多尺度法求解拉索非线性振动问题,得到拉索频率与索力的非线性关系式.对拉索非线性振动频率的公式进行分析,研究初始条件、索力、抗弯刚度及拉索的几何特性对基频的影响,建立索力计算的实用公式并对公式的适用范围进行讨论,将其与目前索力计算公式及有限元分析结果进行比较.结果表明:所获得的基频计算公式简单实用,能同时考虑拉索抗弯刚度与垂度的共同影响,满足精度要求.
Based on the vibration differential equation of axially loaded beam, the nonlinear differential equation of cable vibration considering the dip and bending stiffness of the cable is proposed and multi-scale method is introduced to solve the nonlinear vibration of cable. The relationship between cable frequency and cable The nonlinear relationship of force is analyzed.The influence of initial conditions, cable force, flexural rigidity and cable geometry on the fundamental frequency is studied, and the practical formula of cable force calculation is established. The scope of the formula is discussed and compared with the current cable force formula and the finite element analysis results.The results show that the obtained fundamental frequency formula is simple and practical and can take both the common influence of the bending stiffness and the dip of the cable into account , To meet the accuracy requirements.