温度变化对悬索主共振响应影响分析

摘要

基于增量热场理论,推导考虑均匀温度变化影响下受谐波激励的悬索非线性运动微分方程,利用Galerkin法将方程离散,并对离散后的方程进行线性分析.以悬索主共振响应为例,利用多尺度法求解其高阶近似解及幅频响应方程,通过算例研究温度变化对不同Irvine参数的悬索前四阶模态频率以及幅频响应曲线的影响.研究结果表明:悬索模态振型、频率和主共振响应受温度变化影响明显,且与其Irvine参数密切相关;温度变化有可能定性和定量地改变悬索非线性振动特性,其取决于线性项、平方和立方非线性项系数受温度变化的影响程度;相同程度的升温和降温对悬索振动特性的影响不对称.%Based on the incremental thermal field theory,the nonlinear vibration equations of a suspended cable under harmonic excitation considering uniform temperature variation were derived.Galerkin method was used to discretize the nonlinear vibration equations and the discretized equations were analyzed linearly.The higher order approximate solution and the amplitude-frequency response equation were obtained with the multi-scale method.The effects of temperature changes on the first 4 orders modal frequencies and amplitude-frequency response curves of the suspended cable with different Irvine parameters were studied with numerical examples.The results showed that modal shapes,modal frequencies and primary resonance responses of the suspended cable are obviously affected by temperature changes,and they are closely related to Irvine parameters of the suspended cable;the suspended cable's nonlinear vibration characteristics may be changed quantitatively and qualitatively by temperature effects,they are dependent on the effects of temperature changes on coefficients of the linear term,the square one and the cubic one;the effects of temperature increase and its decrease at the same level on the vibration characteristics of the suspended cable are not symmetric.