含等档的输电线面内自由振动理论

连续档导线运动方程包含平方和立方非线性项，倍频时会产生多模态耦合的复杂响应，因此研究连续档导线模态及共振的频率分布规律尤为重要．基于模态综合法获得了具有相等档距的连续档导线模态函数，基于动刚度理论得到了不同模态对应的频率理论公式，并应用有限元方法验证了模态及频率理论公式的准确性．研究了不同模态对应频率随几何参数的变化趋势，结果表明有相等档距的连续档导线的共振条件和单档导线有明显区别，连续档导线面内对称模态之间容易产生1:1共振，面内对称与反对称模态之间易产生1:2共振．本文研究内容可用来分析连续档导线内共振及其分岔行为．

The Theory for In-Plane Free Vibrations of Transmission Lines Containing a Number of Equal Spans

The motion equations of continuous spans include the quadratic and cubic nonlinearities. Also, interactions between the modes are often responsible for complex dynamical behaviors at double frequency. Therefore, accurate analysis of the distribution of the resonance frequencies and modes of continuous spans is especially important. In this paper, the mode shapes were extracted by modal synthesis method, the formulas of the natural frequencies corresponding to different modes were obtained using dynamic stiffness theory. The accuracy of the mode shapes and formulas of the natural frequencies was verified by finite element method. The geometric parameters-dimensionless frequency curves showed that resonance behaviors of the single span and the continuous spans were obviously different. One-to-two internal resonance is likely to occur between the in-plane symmetric and antisymmetric modes of continuous spans, while one-to-one internal resonance is likely to occur between the in-plane symmetric modes of continuous spans. The results of this paper can be used to analyze the bifurcation and resonance behaviors of continuous spans.