基于最小势能原理的悬索结构动力特性求解与分析  

Solution and analysis for dynamic characteristics of suspension cable structures based on the principle of minimum potential energy

作　　者：赵基达 ZHAO Ji-da(National Engineering Research Center of Building Technology,Beijing 100013,China;China Academy of Building Research,Beijing 100013,China)

机构地区：[1]国家建筑工程技术研究中心,北京100013 [2]中国建筑科学研究院有限公司,北京100013

出　　处：《空间结构》2024年第3期4-11,共8页Spatial Structures

基　　金：中国建筑科学院研究院有限公司院士工作站科研基金项目(20220122330730021)。

摘　　要：对悬索结构的振型函数采用多项正弦函数组合逼近,提出将振型函数分别与竖向结构内力、竖向惯性力的乘积作为结构的总势能.基于最小势能原理,求解单索的动力特性,其结果与伽辽金法求解相同.对对称振型近似采用二项正弦函数组合,以简化方法求得其振型与圆频率.提出了索结构特征参数这一概念,给出了常用垂跨比下索结构特征参数的取值范围.讨论了索结构特征参数变化下单索结构的动力特性,包括单索结构基频振型为反对称双半波振型、第二频率为对称不等高三半波振型、对称振型的双频率及与垂跨比的关系、垂跨比与跨度对单索圆频率的影响等.In this paper,the vibration mode function of a suspension cable structure is approximated by a combination of multiple sine functions,and the product of the vibration mode function for the internal force and inertia force is taken as the total potential energy of the structure.Based on the principle of minimum potential energy,the dynamic characteristics of single cable are solved.The result is the same as that of the Galerkin method.When a combination of two sine functions is used to approximate the symmetric vibration mode,the vibration mode and circular frequency can be obtained by this simplified method.The concept of cable structure characteristic parameter was proposed,and the range of values for cable structure characteristic parameter was given for commonly used sag-to-span ratios.The dynamic characteristics of single cable structures influenced by change of the cable structure characteristic parameter were discussed,including the fundamental frequency vibration mode of single cable structures being antisymmetric double half-wave vibration mode,the second frequency being symmetric unequal height three half-wave vibration mode,the dual frequency of symmetric vibration mode and its relationship with sag-to-span ratio,the influence of the calculation of single cable circular frequency with the sag-to-span ratio and with span,etc.

关 键 词：悬索结构 动力特性 简化计算 最小势能原理 

分 类 号：TU351[建筑科学—结构工程]