索梁结构中抗弯刚度斜拉索的非线性响应

NONLINEAR RESPONSE OF STAY CABLES WITH FLEXURAL RIGIDITY IN CABLE-STAYED BEAMS

研究索梁结构中考虑抗弯刚度斜拉索的非线性响应.从斜拉桥中简化出索梁组合结构力学模型,考虑抗弯刚度、几何非线性及垂度等因素,忽略索梁纵向振动,基于Hamilton变分原理,获得了索梁结构耦合非线性振动偏微分方程组.首先运用Galerkin方法离散该方程组,然后利用多尺度法对该方程组进行摄动分析.以某索梁结构为例,分析了索主要参数对抗弯刚度斜拉索面内基频的影响,探讨了抗弯刚度对斜拉索幅频响应、激频响应的影响,数值模拟获得了索梁结构的时程曲线.结果表明,考虑抗弯刚度后,索长对斜拉索面内基频的影响较大,对于短索,应考虑抗弯刚度;含抗弯刚度斜拉索的幅频响应曲线整体向右平移,激频响应曲线向左移,移动的幅度取决于抗弯刚度的大小;梁振动将对索振动产生显著影响,索振动对梁的振动影响很小.

Considering the flexural rigidity, sagging and geometric nonlinearity, the nonlinear responses of stay cables in cable-stayed beams were investigated. The nonlinear dynamical equations of the cable-stayed beam were formulated by Hamiltonian principle. Then, these equations were discretized by the Galerkin method, and the responses of the cable in the cable-stayed beam were obtained using the Multiple Scales method. The influence of main parameters on the fundamental frequency of the cable in plane was analyzed. The effects of flexural rigidity on both the frequency response and amplitude response were examined. The time history responses of the cable-stayed beam were also obtained by numerical simulations. It was shown that the cable length has a great effect on the fundamental frequency of the cable, and for a short cable, the flexural rigidity should be taken into account. The frequency response curve moves to the right, but the amplitude response curve moves to the left, when the flexural rigidity is considered. The amount of movement depends on the magnitude of flexural rigidity. The vibration of the beam has a significant impact on that of the cable, while the vibration of the cable has little effect on that of the beam.