CAJ | 학술논문

为了进一步准确计算斜拉索的自振频率，考虑斜拉索的重力在弦向的分量对斜拉索非线性振动的影响，分别建立了斜拉索的垂度微分方程和非线性自由振动方程，采用幂级数法求解垂度微分方程，采用伽辽金法把偏微分方程转化为常微分方程，运用摄动法求得该方程的近似解，并制定了相应的数值计算方法，与理论解进行了比较。研究了考虑索力变化影响后拉索的振动特性，采用了更精确的函数来逼近垂度悬链线，解决了考虑重力在弦向的分量时，用抛物线来逼近垂度悬链线时的精度不足的问题。随着索的长度增加，索的总质量也越来越大，因此要考虑斜拉索的重力弦向的分量对斜拉索的振动的影响。
위료진일보준학계산사랍색적자진빈솔，고필사랍색적중력재현향적분량대사랍색비선성진동적영향，분별건립료사랍색적수도미분방정화비선성자유진동방정，채용멱급수법구해수도미분방정，채용가료금법파편미분방정전화위상미분방정，운용섭동법구득해방정적근사해，병제정료상응적수치계산방법，여이론해진행료비교。연구료고필색력변화영향후랍색적진동특성，채용료경정학적함수래핍근수도현련선，해결료고필중력재현향적분량시，용포물선래핍근수도현련선시적정도불족적문제。수착색적장도증가，색적총질량야월래월대，인차요고필사랍색적중력현향적분량대사랍색적진동적영향。
Taking into account the effect of chord component of gravity on the nonlinear free vibration of inclined cables,the nonlinear equations of motion of an inclined cable were developed.The sag differential equation and the nonlinear free vibration equation of the sag were established.The sag differential equation was solved with the method of power series.Galerkin's method was used to convert the nonlinear partial differential equations into ordinary differential equations.The approximate solutions of the equations were obtained with the perturbation method.A corresponding numerical method was developed and the results were compared with the theoretical solution.The vibration characteristics of inclined cables were studied considering the variation of cable forces.A new function was chosen to approximate the catenary sag,which is more precise than the parabola function.The total mass of inclined cable increases with the increasing of the length,so the effect of chord component of gravity on the vibration of inclined cables must be considered.