基于能量变分原理的单向悬索结构固有振动分析

Natural Vibration Analysis of Single-Cable Structure Based Upon the Theory of Energy Variation

固有振动分析是结构动力分析的基础,其目的是计算结构的固有频率和振型。基于能量变分原理提出了单向悬索结构的固有振动分析的简化方法,给出了自振频率和振型的简化计算公式。利用有限元方法对计算结果进行了验证,误差均在5%以内。与传统的Rayleigh法相比,由于考虑了各阶振型之间的相互耦合作用,计算结果更加精确。该方法可用于悬索结构的动力分析,也可作为有限元方法的补充。

Natural vibration analysis was the basis of structural dynamic analysis to obtain the natural frequency and vibration mode. Simplified method for natural vibration analysis of single-cable structure was presented based upon the theory of energy variation. The formulas for natural frequency and vibration mode were given out and the accuracy of the results was validated by finite element method. The error was less than 5% in general. Comparing with Rayleigh method,energy variation method was more accurate because the coupling effect of each vibration mode was considered. The presented method could be used in dynamic analysis of suspension cable as well as the supplement of finite element result.