恒载效应对拱结构自振频率的影响分析

摘要

A spline finite point method was presented to study the natural frequency of arch.The displacement mode shape function of the arch free vibration was simulated with a linear combination of cubic B-spline.The free vibration frequency equation of arch structures was derived according to Hamilton principle,in which the effect of the dead load was considered.Meanwhile,the effect of the dead load on the natural frequency of arch structures was analyzed.The results show that the natural frequency of arch is reduced.The effect of influence depends on the stiffness of the arch itself.When the arch stiffness is certain,the bigger the rise span ration and the radius to thickness ration,the higher the effect of the dead load on the natural frequency of arch structures.%提出用样条有限点法分析拱的自振频率，采用3次B样条函数的线性组合作为位移振型函数，以曲杆变形理论为基础，根据Hamilton原理建立了考虑恒载效应影响时拱的振动频率方程。计算分析了恒载效应对拱结构自振频率的影响。结果表明恒载效应会使拱结构自振频率减小；影响大小与结构自身刚度有关；拱结构截面刚度一定时，拱矢跨比、径厚比越大，恒载效应对自振频率的影响越大。