期刊
MECHANICS BASED DESIGN OF STRUCTURES AND MACHINES
卷 51, 期 7, 页码 4032-4062出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/15397734.2021.1949345
关键词
Nonlinear vibration; cylindrical shell; axially; moving; rotating; stability; normal form
类别
This paper investigates the nonlinear vibration characteristics of rotating axially moving circular cylindrical shells in subharmonic regions and validates the analytical solution using numerical methods. The study reveals that the axial motion and rotation speed intensify the nonlinear behavior of the frequency response.
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.
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