Abstract

The nonlinear vibration characteristics of the rotating axially moving circular cylindrical shells in subharmonic regions are investigated in the present paper. The motion equations are carried out based on the Hamilton principle in cylindrical coordinates utilizing Donnell’s nonlinear shell theory. By introducing the suitable airy stress function, three equilibrium equations in the cylindrical coordinates are simplified into two nonlinear coupled nonhomogeneous PDEs, including a compatibility equation and the transverse motion equation. The compatibility equation solution is obtained employing the seven degrees of freedom for the flexural mode shape of the system. By implementation of the Galerkin method, the motion equation would be projected into seven nonlinear coupled nonhomogeneous ODEs. This set of equations is solved using a direct normal form method validated by the numerical method and available data. The effect of angular velocity and axial speed is investigated employing frequency and force response curves, bifurcation diagrams, time history, and the system’s phase portraits. Always axially moving and rotation speed of the system intensifies the nonlinear behavior of the frequency responses.

摘要

本文研究了旋转轴向运动圆柱壳在次谐波区的非线性振动特性。运动方程是基于哈密顿原理在圆柱坐标系中利用唐纳尔的非线性壳理论进行的。通过引入合适的艾里应力函数，将柱坐标下的三个平衡方程简化为两个非线性耦合的非齐次偏微分方程，包括一个相容方程和一个横向运动方程。利用系统弯曲模态振型的七个自由度获得相容方程解。通过实施 Galerkin 方法，运动方程将投影到七个非线性耦合非齐次常微分方程中。使用数值方法和可用数据验证的直接范式方法求解这组方程。使用频率和力响应曲线、分叉图、时间历程和系统相图研究了角速度和轴向速度的影响。系统的始终轴向移动和旋转速度加剧了频率响应的非线性行为。