梁主共振情形下索梁结构1∶1内共振分析

研究梁产生主共振情形下索梁组合结构的1∶1内共振问题。基于斜拉桥中的索梁组合结构模型,忽略索梁纵向惯性力的影响,考虑弯曲刚度、几何非线性及垂度等因素,利用索梁连接处的变形协调条件,采用Hamilton变分原理建立了索梁结构面内耦合非线性偏微分方程,运用Galerkin离散和多尺度法研究了梁主共振情形下索梁的1∶1相互作用问题,获得了内共振时的平均方程和分叉响应曲线方程。以某斜拉桥中索梁结构参数为例,研究了内共振时索梁结构之间的相互影响及时程曲线。结果表明,索容易出现共振情形,并呈现出较强的非线性特点;梁振动对索振动影响显著,索振动对梁振动影响较小;索梁内共振时能量相互交换,索梁振幅呈现此消彼长的现象。

One-to-one internal resonance of cable-stayed beam in the case of beam primary resonance

The one-to-one internal resonance of cable-stayed beam in the case of beam primary resonance is investigated.The longitudinal inertia force of cable-stayed beam is neglected, the influence of bending rigidity, sagging and geometric nonlinearity on cable are considered during the deduction, the nonlinear partial differential equations of cable-stayed beam are formulated based on Hamiltonian principle.Then, the Galerkin method is used to discretize these equations.Subsequently, the averaged equations and bifurcation equations of 1:1 internal resonance of the cable-stayed beam in the case of primary resonance of the beam are obtained using the Multiple Scales Method as one of the perturbation techniques.A case study of cable-stayed bridge, the interaction and time-history curve between the cable and beam for internal resonance are analyzed.As a result, the cable is easy to appear the resonance, and the vibration is strong nonlinear characteristics; the vibrations of beam have a significant impact on the vibration of cable, while the vibrations of cable have little effect on that of beam; the energy exchanges between the cable and the beam when the system appear internal resonance, in addition, the amplitude of the cable increased with the decrease of the amplitude of the beam in the course of internal resonance.