受压旋转梁在弹性支承双参数激励作用下的振动特性  

Vibration characteristics of a compressed spinning beam underthe action of two-parameter excitation of elastic support

作　　者：孙强强 杜长城[1] 蒋娜 SUN Qiangqiang;DU Changcheng;JIANG Na(School of Mechanical Engineering,Southwest Petroleum University,610500 Chengdu,China)

机构地区：[1]西南石油大学机电工程学院,成都610500

出　　处：《应用力学学报》2024年第6期1403-1410,共8页Chinese Journal of Applied Mechanics

摘　　要：研究了受压旋转细长梁在弹性支承下的参数动力学行为。针对受恒轴力作用的旋转Rayleigh梁,考虑其一端弹性支承和另一端简支约束,采用Hamilton原理得到了此旋转梁的偏微分运动方程,通过伽辽金法得到了广义模态坐标的运动方程。采用多尺度法分析了此受压旋转Rayleigh梁在弹性支承激励下的参数振动特性。分析了梁在不同参数下的失稳类型与失稳的形式,绘制了系统在弹性支承参数激励下的稳定图,着重探讨了弹性支承边界对梁系统稳定区造成的影响。结果显示系统的参数共振包含两种形式:主共振和组合共振。稳定图反映了转速和外加载荷在弹性支承激励下对系统的稳定区的影响。The parametric dynamical behavior of a spinning slender beam under elastic support is studied.A spinning Rayleigh beam under constant axial force is considered,sustained by an elastic support at one end and a simply support at the other end.The dynamical model is obtained based on the Hamilton principle,and the motion equations for the generalized mode coordinates are derived through the Galerkin method.The parametric vibration characteristics of the spinning Rayleigh beam with elastic support are analyzed according to the multiple scale method.The instability type and form of the beam under different parameters are analyzed,and the stability diagram of the system under the excitation of elastic support parameters is drawn.The effect of the elastic support boundary on the stability zone of the beam system is emphasized.The results show that the system contain two types of parametric resonance:main resonance and combined resonance.The stability diagram reflects the influence of the speed and the external load on the stability zone of the system under the excitation of the elastic support.

关 键 词：弹性支承 旋转Rayleigh梁 多尺度法 参数激励 

分 类 号：O323[理学—一般力学与力学基础] O326[理学—力学]