旋转Rayleigh梁在轴向力下的参数稳定性  

Parametric stability of spinning Rayleigh beam under axial force

作　　者：熊春 杜长城[1] 杨高峰 Xiong Chun;Du Changcheng;Yang Gaofeng(School of Mechatronic 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》2020年第5期2176-2182,I0024,共8页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金项目(11602208;51674216;11702230)。

摘　　要：研究了旋转Rayleigh梁在周期脉动的轴向力作用下的参数振动特性。基于哈密顿原理建立了考虑周期时变轴向力的旋转Rayleigh梁的动力学模型,进而采用Galerkin法得到了关于模态坐标的时域常微分方程。借助多尺度法,得到了参数振动存在的共振条件。分别讨论了轴向力、模态阶数和长细比对系统稳定区的影响,得到了系统的临界失稳曲线。研究表明:细长旋转梁的参数振动有超谐波共振和组合共振两种共振形式;轴向力、长细比对系统的稳定区的位置、大小均有影响,阶数仅对稳定区的位置有影响。The parametric vibration characteristics of a spinning Rayleigh beam subjected to periodic pulsated axial forces are studied. The dynamic model of the spinning Rayleigh beam under action of periodic axial force is established based on the Hamiltonian principle. And then the time domain ordinary differential equations of modal coordinates are obtained by the Galerkin method. By using the multiple-scale method, the resonance conditions of the parameter vibration are obtained. The effects of axial force, modal order and slenderness ratio on the stability zone of the system are discussed respectively, and the transition curve of the system is obtained. It is found that the parametric vibration of the slender spinning beam has two forms of resonance: super harmonic resonance and combined resonance;the axial force and slenderness ratio will regulate the position and size of the stable region of the system, while the modal order only affects the position of the stable region.

关 键 词：细长旋转梁 轴向力 多尺度法 参数稳定性 

分 类 号：O323[理学—一般力学与力学基础] O326[理学—力学]