直接法与间接法对拉索耦合内共振的影响研究

Influence of direct method and indirect method on internal resonance of cable

首先基于哈密顿变分原理推导了考虑抗弯刚度影响的拉索二自由度控制微分方程,然后分别采用直接法与间接法处理动张力,结合MATLAB软件对比这两种计算方法对控制微分方程中系数的影响。采用多尺度法分析了拉索可能存在的内共振模式,结合数值法分析了直接法与间接法对拉索振幅的影响,最后对比了两种计算方法下抗弯刚度对拉索幅值造成的影响。针对某座桥梁的斜拉索进行参数分析,其参数分析结果表明:两种计算方法下控制微分方程中系数的大小都随着拉索跨径的增加而减小,其中系数b5、b5’、b6、b6’、c5、c5’的值在跨径到达30m时趋于稳定不再变化,系数b4、b4’、b8、b8’、b9、b9’、c6、c6’、c7、c7’的值在跨径到达10m时趋于稳定不再变化,且两种计算方法所得系数的比值接近1.5。内共振分析表明,直接法与间接法不会影响拉索耦合共振的幅值,抗弯刚度对拉索幅值的影响仅为0.11%。

Based on the Hamiltonian variational principle,the differential equations of two degrees of freedom of cable considering the influence of bending stiffness are derived,and then direct method and indirect method are used to deal with the dynamic tension respectively.The influence of these two methods on the coefficients of the governing differential equation is compared with the one via MATLAB software.In this paper,the internal resonance of cable is analyzed by method of multiple time scales,and the influence of direct method and indirect method on displacement response of cable is analyzed by numerical method.Finally,the influence of bending stiffness on displacement response of cable under the two calculation methods is compared.The results of parameter analysis show that the coefficients in the governing equations decrease with the increase of the span of cable,among which the coefficients b5,b5’,b6,b6’and c5,c5’tend to be stable when the span reaches 30 m,and the coefficients b4,b4’,b8,b8’,c6,c6’and c7,c7’tend to be stable when the span reaches 10 m,and the ratio of the coefficients obtained by the two calculation methods is close to 1.5.The internal resonance analysis shows that the direct method and the indirect method will not affect the displacement response of the cable,and the bending stiffness will not seriously affect the displacement response of the cable.