论文部分内容阅读
为研究斜拉桥主梁纵向漂移对拉索非线性振动的影响,利用Galerkin方法得到了两端激励拉索的离散运动方程,再用Matlab和DSolver分别求解,两者结果完全吻合。绘制了激励-响应关系图,分别研究两种纵向漂移频率(主共振和亚谐波共振)时固结体系、小幅纵向漂移和大幅纵向漂移三种情况下斜拉索非线性振动。结果表明:合理的主梁纵向漂移可有效减小斜拉索振动;斜拉索本质上只存在参数激励和强迫振动两种激励模式,在亚谐波共振时这两种激励模式互不影响。不论斜拉索角度,端部激励大小及方向如何变化,只要各激励在斜拉索轴向分量之和(参数激励)及横向分量之和(强迫振动)不变,则斜拉索响应不变。
In order to study the influence of longitudinal drift of cable-stayed bridge on the nonlinear vibration of cable, the discrete equations of motion of the cable at both ends are obtained by Galerkin method and solved respectively by Matlab and DSolver. The results agree well with each other. The excitation-response diagram is plotted to study the nonlinear vibration of stayed cables under three kinds of longitudinal drift frequency (main resonance and subharmonic resonance), the consolidation system, small longitudinal drift and large longitudinal drift respectively. The results show that: a reasonable longitudinal drift of the main girder can effectively reduce the vibration of the stay cable; there are only two types of excitation modes: the parametric excitation and the forced vibration. The two excitation modes do not affect each other in the subharmonic resonance. Regardless of the angle of the stay cables, the size and direction of the end excitations vary, the stay cables stay the same as long as the sum of the axial components of the stay cables (parametric excitation) and the sum of the lateral components (forced vibration) .