【作者】 赵磊；

【导师】 扶名福；

【作者基本信息】 南昌大学 ， 力学， 2011， 硕士

【摘要】 公路桥梁动力学是现代公路桥梁发展的一个重要课题,尤其是近来的地震发生,使不少桥梁被破坏甚至倒塌,当然主要的原因有构造设防问题,也有桥梁带病工作问题等。支座是连接桥梁上部结构和下部结构的重要构件,历来被认为是桥梁整体抗震性能上的一个薄弱环节,它的破坏会直接影响到梁体和桥墩的安全性。因此研究带缺陷支座桥梁的振动分析具有一定的工程指导意义。本文考虑支座弹性模量和横截面积受损,通过对弹簧损伤基本关系的推导,把缺陷支座简化为弹簧支承模型,介入损伤因子的概念,得出弹簧损伤后的刚度与未损伤时的刚度关系式k=k(1-DA)(1-DE)。结合损伤力学和桥梁动力学基本原理分别对带缺陷支座的悬臂梁桥、连续梁桥和拱桥进行了振动分析。本文研究中的具体工作和成果有：1、在初等梁弯曲振动方程基础上,引入损伤的概念分别推导了存在竖直刚度缺陷和水平刚度缺陷单跨悬臂梁的振型函数和固有频率方程；并运用转换矩阵法分别推导了中间带缺陷支座的两端固定以及一端固定、一端自由的多跨悬臂梁的振型函数和固有频率方程；得出了移动质量激励下带竖直刚度缺陷支座悬臂梁桥的位移响应。2、运用Laplace变换和逆变换推导了两端刚性铰支、中间带缺陷支座的一般情况下连续梁的振型函数和固有频率方程,并导出了考虑轴力时的振型函数和固有频率方程及弹性失稳时的屈曲荷载特征方程；计算分析了支座损伤程度对连续梁固有频率的影响；讨论了不同支座情况下的动力特性。运用振型正交性,得出了带缺陷支座连续梁桥在简谐激励作用下的位移响应方程。3、推导了存在水平刚度缺陷支座拱桥的平面挠曲平衡方程；考虑拱桥的固有振动并借助Matlab软件绘制了拱脚产生的水平推力与损伤因子的关系曲线。曲线表明：随着损伤程度的加大,水平推力值下降比较快；分析了匀速简谐力作用下的水平刚度缺陷支座拱桥的位移响应,推导了匀速移动双轴汽车荷载作用下的缺陷支座拱桥的动力响应。更多还原

【Abstract】 Highway bridge dynamics is an important topic of the development of modern roads and bridges, especially in the recent earthquakes, so many bridges were damaged or even collapse, of course, the main reasons are structural fortification issues, bridge work with defects, etc. Bridge supports which have long been considered a weak link of the overall seismic performance of the bridge are important components that connect the superstructure and substructure of the bridge, and its damage will directly affects the safety of the beam and pier. Therefore, the research on the vibration analysis of bridges with defective supports has certain engineering significance.This paper considers the damage of elastic modulus and cross sectional area, through the derivation of basic relations of spring damage, the defective support is simplified to spring supporting model, and involved the concept of damage factor, we can get the relationship of spring stiffness before and after injury: k-k(1-DA)(1-DE).We did vibration analysis of cantilever Beam Bridge, continuous beam bridge and arch bridge with the combination of damage mechanics and the basic principles of bridge dynamics. In this paper, the specific work and achievements are:1. On the basis of bending vibration equation of elementary beam, we introduce the concept of injury, and get the mode function and natural frequency equation of single span cantilever with the condition of the vertical stiffness defects and horizontal stiffness defects; and use the conversion matrix method, we get the mode function and natural frequency equation of multi-span cantilever beam fixed at both ends and one end fixed, the other end free, but there is a defective support in the middle of the beam; obtained the displacement response of cantilever bridge with support has a vertical defective stiffness under the moving mass.2. Use the Laplace transform and inverse transform, under normal circumstances, we got the mode function and natural frequency equation of continuous beam with rigid hinged at both ends and there is a defective support in the middle of the beam, got the mode function,natural frequency equation when considering the axial force and the buckling load characteristic equation when elastic buckling; got the influence of the degree of support damage to the natural frequency of continuous beam by calculating; discussed the dynamic characteristics of bridge with different supports. Use the orthogonal modes; we got the displacement response equation of the continuous beam bridge with defective supports in the harmonic excitation.3. We also deduced the balance equation of plane bending of arch bridge with horizontal defective stiffness supports; consider the natural vibration of the bridge, then use Matlab we can got the curve of arch thrust and injury factor. Curve shows that:with the injury increased, the level of thrust value decreased faster. We got the affect of horizontal defective stiffness supports to the displacement response of arch bridge under harmonic force, deduced the dynamic response of arch bridge with defective supports under uniform velocity biaxial moving vehicle load.更多还原