变截面粘弹性旋转梁非线性参数振动研究  

STUDIES ON NONLINEAR PARAMETRIC VIBRATION OF A ROTATING VISCOELASTIC BEAM WITH VARIABLE CROSS-SECTIONS

作　　者：张云飞 杨鄂川 李映辉[1] Zhang Yunfei;Yang Echuan;Li Yinghui(School of Mechanics and Engineering,Southwest Jiaotong University,Chengdu 610031,China;School of Mechanical Engineering,Chongqing University of Technology,Chongqing 400054,China)

机构地区：[1]西南交通大学力学与工程学院,成都610031 [2]重庆理工大学机械工程学院,重庆400054

出　　处：《动力学与控制学报》2018年第5期418-423,共6页Journal of Dynamics and Control

摘　　要：研究了变截面粘弹性旋转梁的非线性参数振动.基于Kelvin-Voigt粘弹性本构关系,考虑几何非线性建立了变截面粘弹性旋转梁的非线性振动方程,用Galerkin法将其转化为常微分方程.运用多重尺度法得到其幅频响应.用数值方法讨论了转速和轮毂半径对梁固有频率和幅频响应的影响.研究表明:不稳定域随轮毂半径、转速的增大而增大,随锥度的增大而减小.Nonlinear parametric vibration of a rotating viscoelastic beam with variable cross-section is studied.Nonlinear governing equation of the rotating viscoelastic beam with variable cross-section involving geometric nonlinearity is established based on Kelvin-Voigt constitutive relation. The governing equation is then transformed into an ordinary differential equation by using Galerkin method. Amplitude-frequency response is obtained by adopting the method of multiple scale. Finally,the influences of rotating velocityand radius of the hub on nature frequency and amplitude-frequency response are numerically discussed. It is shown that the unstable region increases with the increasing rotating velocity and radius of hub,but decreases with the increasing taper of the beam.

关 键 词：变截面梁 参数振动 多重尺度法 非线性 幅频响应 

分 类 号：O322[理学—一般力学与力学基础]