摘要
In this paper, nonlinear transverse vibrations of axially moving Timoshenko beams with two free ends are investigated. The governing equations and the associated boundary conditions are derived by the extended Hamilton principle. The method of multiple scales is applied to analyze the nonlinear partial differential equation. The natural frequencies and modes are investigated by performing the complex mode approach. The effect of natural frequencies with the stiffness and the axial speeds are numerically demonstrated. The solvability conditions are established for the cases of without and with 3:1 internal resonances. The relationships between the nonlinear frequencies and the initial amplitudes at different axial speeds and the nonlinear coefficients are showed for the case of without internal resonances. The effects of the related coefficients are demonstrated for the case of 3:1 internal resonances.
In this paper, nonlinear transverse vibrations of axially moving Timoshenko beams with two free ends are investigated. The governing equations and the associated boundary conditions are derived by the extended Hamilton principle. The method of multiple scales is applied to analyze the nonlinear partial differential equation. The natural frequencies and modes are investigated by performing the complex mode approach. The effect of natural frequencies with the stiffness and the axial speeds are numerically demonstrated. The solvability conditions are established for the cases of without and with 3：1 internal resonances. The relationships between the nonlinear frequencies and the initial amplitudes at different axial speeds and the nonlinear coefficients are showed for the case of without internal resonances. The effects of the related coefficients are demonstrated for the case of 3：1 internal resonances.
基金
supported by the National Outstanding Young Scientists Foundation of China (Grant No. 10725209)
the National Natural Science Foundation of China (Grant No. 90816001)
Shanghai Subject Chief Scientist Project (Grant No. 09XD1401700)
Innovation Foundation for Graduates of Shanghai University (Grant No. A.16-0401-08-005)
Shanghai Leading Academic Discipline Project (Grant No. S30106)
the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0844)
