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在侧向风力或侧向水平地源力作用下,斜拉桥容易发生扭转振动。本文采用非线性Rayleigh阴尼,它能反映在低速振动时有激发而加速振动,至一定高速后又衰减的完整振动过程。对非线性的统辖方程及定解条件,先使之无量纲化,再按非线性项的系数这个小参数展开未知函数,得到线性化的各级近似方程。把待求函数展成梁轴坐标的Fourier级数,其系数为待定的时间函数,应用Fourier级数的正交性,得到求解未知时间函数的二阶常微分方程,完全类似单自由度质点在线性粘滞性阻尼作用下的统辖方程,其解为已知。
Under lateral wind or lateral horizontal source force, the cable-stayed bridge is prone to torsional vibration. In this paper, a non-linear Rayleigh-type nephelometer is used, which can reflect the complete vibration process of exciting and accelerating vibration at low speed and reaching a certain high speed and then decaying. For non-linear governing equations and solution conditions, we first make them dimensionless, and then expand the unknown function according to the small parameter of the nonlinear term, to get the linearized approximate equations at all levels. The function to be solicited into the Fourier series of beam axis coordinates, the coefficient for the time function to be determined, the application of Fourier series of orthogonality, obtained for solving unknown time functions of second-order ordinary differential equations completely similar to the single-degree-of-freedom particle online The governing equation under the action of viscous damping is known.