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斜拉桥塔−索−梁耦合面内整体动力学模型与1:1内共振影响性分析

MODELLING AND ANALYSIS OF THE IN-PLANE DYNAMICS OF CABLE-STAYED BRIDGES CONSIDERING THE PYLON-CABLE-BEAM COUPLING EFFECT

  • 摘要: 为研究塔−梁模态间耦合作用对斜拉桥整体模态及1:1内共振影响, 考虑由斜拉索初始垂度及横向振动大位移引起的几何非线性, 建立固结体系斜拉桥塔−索−梁耦合面内整体动力学模型. 其中桥塔和主梁被简化为参数质量体系, 基于塔−索、索−梁及塔−梁动态平衡关系推导得到斜拉桥整体模型的动力平衡方程. 通过有限差分法对参数体系的微分方程进行代数转换, 运用模态拖拽法和分离变量法得到结构的运动方程和模态函数, 观察到局部−整体模态间、主导−非主导模态间的模态翻转现象, 并采用Runge-Kutta积分方法对无阻尼的系统方程进行数值仿真, 系统分析了塔−梁耦合作用对1:1内共振的影响, 结果表明: 在文章塔−索−梁耦合模型中, 塔−梁耦合作用对结构的低阶对称及高阶整体模态没有影响作用, 塔或梁的振动模态完全主导了该阶结构整体模态; 塔−梁耦合作用对结构的低阶反对称整体模态具有显著影响作用, 此时结构整体模态呈现为塔和梁振动模态共同参与的混合整体模态. 拉索的振动模态与此两种整体模态1:1耦合都将产生剧烈内共振, 各构件的模态局部化程度系数是量化内共振参与度的重要因素. 在完全整体模态内共振中, 非主导模态不参与结构内共振, 能量转换仅发生在主导的构件模态与拉索的振动模态间; 在混合整体模态内共振中, 非主导模态将参与内共振能量转换并改变拉索振动响应的动力特性, 其影响效应随整体模态阶次与构件参数变化而变化.

     

    Abstract: To study the pylon-beam modal coupling effect on the global modes and 1:1 internal resonance of rigid-frame cable-stayed bridges, a novel in-plane dynamic model, considering the geometric nonlinearity caused by cables’ initial sag and lateral large displacement, is established in this paper. The bridge pylon and beam in the model are modelled as integrated systems consisting of discretized parametric segments. The dynamic equations of the whole structure are derived based on the dynamic connections between the pylon-cable, cable-beam, and pylon-beam nodes. Using the finite difference method, the dynamic balance differential equations of the parametric system are transformed algebraically. The whole bridge governing equations and modal functions are obtained through the modal drag method and variable separation method. Based on the simulation of the undamped equations via Runge-Kutta method of 4 ~ 5-order, the modal veering phenomena between local-global modes and dominant-nondominant modes are observed. The simulation results shows that pylon-beam modal interaction has no significant effect on the low-order symmetric and high-order global modes of the structure, for which completely dominated by the local modes of the pylon or beam is complete global mode. Moreover, it is obtained that the local modes of the pylon or beam have a significant effect on the low-order anti-symmetric global modes, for which jointly dominated by both pylon and beam modes is hybrid global modes. It is verified that the coupling 1:1 internal resonance is excited when the local modal frequency of the cable meets both types of global modes. The localized factor of each component in the global modes plays an important factor in measuring the degree of internal resonance participation. In a complete global mode internal resonance, non-dominant modes do not participate in the internal resonance of the structure, and energy conversion occurs only between the dominant component mode and the cable local mode. In a hybrid global mode internal resonance, non-dominant modes participate in internal resonance and would change the dynamic characteristics of the cable vibration response. The influence varies with the order of global modes and cable mechanical parameters.

     

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