悬索面内次谐波共振受温度效应影响研究

Investigation of temperature effects on the in-plane sub-harmonic resonances of suspended cables

整体均匀温度变化会导致悬索形成新的热应力构型,影响张拉力和垂度大小。温度变化对于悬索非线性动力学方程的影响可通过与索力和垂度相关的两个无量纲参数体现。基于考虑温度变化影响下的悬索面内非线性动力学方程,利用Galerkin法对运动方程进行离散,运用多尺度法求解1/2和1/3单模态面内次谐波共振响应的近似解,并得到了相应的幅频响应方程,通过数值算例从定性和定量的角度探究温度变化对其共振响应的具体影响。算例研究表明温度变化对悬索次谐波共振响应特性影响明显,且不同垂跨比的悬索其振动特性受温度变化的影响有区别。当垂跨比较小时,一定程度的温度变化会导致其振动特性发生定性和定量的改变,改变幅频响应曲线的偏转方向及程度,影响共振区间及响应幅值。当垂跨比进一步增加后,温度变化仅会产生定量影响,改变幅频响应曲线偏转程度,影响系统共振幅值。由于悬索存在初始张拉力,相同程度的升温和降温对悬索次谐波振动特性的影响不对称。

A new thermal stressed configuration of suspended cables was generated under the effects of temperature variations which lead to some changes of the cable tension force and sag.The effects of temperature changes on the nonlinear equations of motion of a suspended cable are reflected by two non-dimensional factors related to the cable tension and sag.On the basis of the nonlinear in-plane vibration equations of the suspended cable under harmonic excitation where the temperature effects were taken into consideration,the Galerkin method was introduced to discretize the nonlinear partial differential equations firstly,then the multiple scales method was used to obtain the approximate solutions of1/2and1/3order sub-harmonic resonances,and the corresponding frequency response equations were obtained.Furthermore,the temperature effects on the resonance responses were investigated quantitatively and qualitatively by using numerical examples.The numerical results show that the effects of different temperature variations on the sub-harmonic resonances of the suspended cable are obvious,and these effects are closely related to the sag-to-span ratio.As to the case of small sag-to-span ratio,the nonlinear vibration characteristics would be varied by the temperature effects quantitatively and qualitatively,and the deflection and its degree of the frequency response curves are changed under the temperature effects,and the range of resonances and the response amplitudes are also affected.As to the case of large sag-to-span ratio,only some quantitatively changes are induced by the temperature variations,and the response amplitudes are altered.Due to the initial tension force,the effects of warming and cooling on the nonlinear sub-harmonic vibration behaviors of the suspended cable are not symmetric.