不同加劲梁重量下的悬索非线性振动特性

悬索桥因受力明确、跨越能力大、结构美观等特点而被广泛应用。加劲肋重量是影响悬索桥静态构型及其动力学特性的主要因素。为研究不同加劲梁重量下悬索桥的固有特性及其非线性动力学行为。建立了悬索结构的非线性动力学模型。首先，将运动方程退化至保留线性项，探究加劲梁重量对悬索固有特性的影响；然后，再进一步揭示加劲梁重量对1:1内共振、响应时程和瞬时相频特性三种非线性振动特性的影响。研究表明：面内正对称频率的变化与加劲梁重量变化呈反比关系，且交叉点位置会随加劲梁增大而移向Irvine参数变大的方向，阶次越高越显著。此外，加劲梁重量逐渐增大将使悬索由硬弹簧变为软弹簧，并使面内1阶振幅与加劲梁重量由正相关变为负相关。加劲梁重量变化还将导致面内响应复平面投影曲线轨迹变化，进而表现出不同的相频特性。

Nonlinear vibration characteristics of suspended cables under different stiffening girder weight

Suspension bridge is widely used because of its clear force, large spanning capacity and beautiful structure. The weight of stiffening girder is the main factor affecting the static configuration and dynamic characteristics of suspension bridge. In order to study the natural characteristics and nonlinear dynamic behavior of suspension bridge under different stiffening girder weights, a nonlinear dynamic model of suspended cable is established. First, the equations of motion are reduced to linear terms, and the influence of the stiffening girder weight on the natural characteristics of the suspended cable is investigated. Then, the influences of the stiffening girder weight on the three nonlinear vibration characteristics of 1:1 internal resonance, response time history and instantaneous phase-frequency characteristics are further revealed. The results shown that the change of the in-plane symmetric frequency is inversely proportional to the variation of the stiffening girder weight. The position of the intersection moves to large Irvine parameter as the stiffening girder weight increasing, and the higher the order is, the more significant it is. In addition, with the increasing of the weight of the stiffening girder, the stiffness of the suspended cable changes from hard spring property to soft spring property. Meanwhile, the relationship between the in-plane first-order amplitude and the weight of the stiffening girder changes from positive correlation to negative one. The change of the stiffening girder weight also leads to the variation of the curve trajectories of the complex plane projections of the in-plane responses, and thereby showing different phase-frequency characteristics.