横向载荷作用下轴向运动梁的屈曲失稳以及非线性振动特性

梁的轴向运动会诱发其产生横向振动并可能导致屈曲失稳，对结构的安全性和可靠性产生重大的影响。本文重点研究了横向载荷作用下轴向运动梁的屈曲失稳及横向非线性振动特性。基于Hamilton变分原理，建立了横向载荷作用下轴向运动梁的动力学方程，获得了梁的后屈曲构型。使用截断Galerkin法，将控制方程改写成Duffing方程的形式。用同伦分析方法确定载荷作用下轴向运动梁的非线性受迫振动的封闭形式的表达式。结果表明，后屈曲构型对轴向速度和初始轴向应力有明显的依赖性。通过同伦分析法得出非线性基频的显式表达式，获得了初始轴向力会影响非线性频率随初始振幅和轴向速度的线性关系。另外，轴向外激励的方向也会改变系统固有频率。

Buckling instability and transverse nonlinear vibration characteristics of axially moving beams under load

The axial movement of the beam will induce lateral vibration and may lead to buckling instability, which has a significant impact on the safety and reliability of the structure.This paper focuses on the buckling instability and nonlinear transverse vibration characteristics of the axially moving beams under load.Based on Hamilton variational principle, the dynamic equation of the axially moving beam under transverse load is established, and the post buckling configuration of the beam is obtained.Using truncated Galerkin method, the governing equation is rewritten into the form of Duffing equation.The closed form expression of nonlinear forced vibration of the axially moving beam under load is obtained with homotopy analysis method.The numerical results show that the post buckling configuration is obviously dependent on the axial velocity and initial stress.Through the explicit expression of nonlinear fundamental frequency obtained byhomotopy analysis method, it is obtained that initial axial force will affect the linear relationship of nonlinear frequency with respect to initial amplitude and axial velocity.In addition, the direction of shaft outward excitation will also change the natural frequency of the system.