考虑弯曲刚度斜拉索面内面外内共振分析

本文研究桥梁工程中含弯曲刚度斜拉索的面内面外内共振问题．描述了工程中斜拉索变形的三种状态，考虑弯曲刚度、大变形及垂度等因素，忽略斜拉索纵向惯性力的影响，运用Hamilton变分原理建立了含弯曲刚度的斜拉索面内面外耦合偏微分控制方程，采用Galerkin方法对偏微分方程离散，并运用多尺度摄动方法进行了求解，获得了斜拉索可能存在的内共振模式，以工程中一根斜拉索为例，运用有限元法对其进行动力特性分析，列出了斜拉索前10阶面内面外振动频率，找出面内面外可能产生内共振的模态，分别研究了主共振条件下斜拉索面内和面外1:1、2:1内共振情形，获得了有意义的结论．

In-Plane and Out-of-Plane Internal Resonance of Stay Cables Considering Bending Stiffness

The in-plane and out-of-plane internal resonance of stay cables considering bending stiffness in bridge engineering are investigated. Three kinds of deformation states in engineering are described. The partial differential equations governing the in-plane and out-of-plane vibration of the stay cable are derived using Hamiltonian principle considering bending stiffness, large deformation and sag, with the influence of the longitudinal inertia force neglected. The Galerkin Method is used to discretize the partial differential equations, then the method of multiple scales is employed to solve the governing equations to obtain the possible modes of internal resonance. Taking one stay cable in engineering for example, the finite element method is applied to get the dynamic characteristics of the stay cable. The first 10 in-plane and out-of-plane natural frequencies are listed, and the possible in-plane and out-of-plane internal resonance modes are sought. The primary resonance situations with the in-plane to out-of-plane ratio as 2:1 and 1:1 are also investigated. In the end, some meaningful conclusions are drawn.