考虑温度效应的悬索超谐波共振响应研究  

Investigation of Super-harmonic Resonance Response of Suspended Cables Considering Temperature Variation Effects

作　　者：赵珧冰[1] 金波[2] 赵跃宇[2] 黄超辉 ZHAO Yaobing;JIN Bo;ZHAO Yueyu;HUANG Chaohui(College of Civil Engineering,Huaqiao University,Xiamen 361021,China;College of Civil Engineering,Hunan University,Changsha 410082,China)

机构地区：[1]华侨大学土木工程学院,福建厦门361021 [2]湖南大学土木工程学院,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2018年第5期29-35,共7页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(11602089);湖南省交通厅科技项目(201525);福建省自然科学基金青年创新项目(2016J05011);福建省教育厅中青年教师教育科研项目(JAT160025);华侨大学中青年教师科研提升资助计划项目(ZQN-YX505)~~

摘　　要：引入与张拉力和垂度相关的无量纲参数,可推导出整体温度变化影响下悬索面内非线性运动微分方程.首先利用Galerkin法得到离散后的无穷维方程,然后运用多尺度法求解其二阶和三阶单模态超谐波共振响应的近似解,并得到幅频响应方程,最后通过数值算例探究三种垂跨比的悬索,温度变化对其单模态超谐波共振响应的影响.研究结果表明:当垂跨比较小时,一定程度的温度变化会导致其超谐波共振响应发生定性和定量的改变,改变系统软硬弹簧的性质和程度,即改变其幅频响应曲线的偏转方向和程度;温度变化会改变激励-响应幅值曲线的单值/多解情况.然而当垂跨比逐渐增大后,温度变化对其共振响应仅会产生定量的影响,且温度变化与幅频响应曲线向左偏转程度呈正比,即温度上升,曲线向左偏转程度加剧,软弹簧特性增强,反之则减弱.由于悬索存在初始张拉力,升高和降低相同温度对超谐波共振特性影响呈现出不对称性.By introducing two non-dimensional parameters related to the cable tension force and sag,in-plane nonlinear equations for motion of the suspended cable considering the temperature effect were derived.Firstly,the nonlinear partial differential equation was discretized by the Galerkin method.Then,the approximate solutions of the second and third order single mode super-harmonic resonances of the suspended cable were obtained by the multiple scales method,and the corresponding frequency response equations were also derived.Finally,the effect of temperature variations on the single mode super-harmonic resonances of the suspended cable with three different sag-to-span ratios was illustrated by the numerical calculations.The numerical results show that：in the case of small sag-to-span ratio,the nonlinear vibration characteristics would be changed by a certain degree of the temperature change quantitatively and qualitatively,the softening and hardening spring behaviors are changed,and it means that the degree and direction of the frequency response curves are changed.The single/multi-values of the excitation-response amplitude curves are also varied by the temperature variations.However,with the increase of the sag-to-span ratio,only some quantitative changes are found under the thermal effect.With the increase of the temperature change,the frequency response curves are bent to the left much more,and the softening spring characteristic is also increased.Moreover,due to the initial tension force of the suspended cable,the effects of warming and cooling conditions on the vibration characteristics of the suspended cable are not symmetric.

关 键 词：悬索 温度变化 多尺度法 振动特性 超谐波共振 幅频响应曲线 

分 类 号：U441.3[建筑科学—桥梁与隧道工程] U448.35[交通运输工程—道路与铁道工程]