国家自然科学基金资助项目(10272117),广东省自然科学基金资助项目(011203)
应用增量谐波平衡法(IHB法)研究轴向运动梁横向非线性振动的内部共振.根据哈密顿原理建立非惯性参考系下轴向运动梁的横向振动微分方程,采用分离变量法分离时间变量和空间变量并利用Galerkin方法离散运动方程,再应用IHB法进行非线性振动分析,研究了在固有频率之比ω20/ω10接近于3:1情况下,外激励频率ω在ω10,ω20附近的具有内部共振的基谐波和次谐波响应.数值结果表明了IHB法是一个求解轴向运动体系非线性振动的非常有效的半解析、半数值的方法.
The laterally nonlinear vibration of axially moving beams weve analyzed by the incremental harmonic balance(IHB) method.Firstly the motion equations of an axially moving beam weve derived by Hamilton's principle,Then the Galerkin method was used to discretize the governing equations.Finally, the IHB method was employed to solve the nonlinear vibration equations.Particular attention was paid to the fundamental,subharmonic resonance with internal resonance under the condition ω20/ω10≈3 as ω is near ω20,ω10,where ω is the forcing frequency,and ω10 and ω20 are the first and the second natural frequencies.The number results show that the IHB method is a very effective semi-analytical and seminumerical method for nonlinear vibration of axially moving system.
陈树辉,黄建亮,余锦炎.轴向运动梁横向非线性振动研究[J].动力学与控制学报,2004,2(1):40~45; Chen Shuhui, Huang Jianliang, She Jinyan. Study on the laterally nonlinear vibration of axially moving beams[J]. Journal of Dynamics and Control,2004,2(1):40-45.
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