摘要
基于大位移非线性弹性理论的广义变分原理,考虑了加劲梁的压弯耦合、剪切应变能和扭转应变能的影响,建立了三跨自锚式悬索桥空间耦合自由振动的大位移不完全广义势能泛函,通过对竖向位移约束变分,推导出自锚式悬索桥的竖向挠曲振动微分方程,忽略非线性项的影响,进而得到线性振动微分方程。以一座主跨240m混凝土自锚式悬索桥为例,求出了竖向振动方程自振频率的解析解,并与数值解作了比较,吻合较好。这一理论和方法为自锚式悬索桥的固有振动特性分析提供可靠的理论依据。
Based on the generalized potential energy variational principle of nonlinear elasticity theory with large deflection, an incomplete generalized potential energy functional for free vibrations of three-span self-anchored suspension bridges is established by considering the coupling of flexural and axial deformation, shear strain energy and torsion strain energy of stiffening girder. Neglecting nonlinear terms, the linear vertical vibrational differential equations are obtained through constraint variation. A concrete self-anchored suspension bridge with main span of 240 meters is taken as an example. The analytical results of frequency coincide with those of numerical methods. It is believed that the present method can provide a theoretical basis for the analysis of free vibrations of self-anchored suspension bridges.
出处
《工程力学》
EI
CSCD
北大核心
2005年第4期126-130,共5页
Engineering Mechanics
关键词
自锚式悬索桥
压弯耦合
自由振动
泛函
广义变分
self-anchored suspension bridge
coupling of flexural and axial deformation
free vibration
functional
generalized variation
