Kinematic Aspects in Modeling Large-Amplitude Vibration of Axially Moving Beams

Abstract

This paper clarified kinematic aspects of motion of axially moving beams undergoing large-amplitude vibration. The kinematics was formulated in the mixed Eulerian–Lagrangian framework. Based on the kinematic analysis, the governing equations of nonlinear vibration were derived from the extended Hamilton principle and the higher-order shear beam theory. The derivation considered the effects of material parameters on the beam deformation. The proposed governing equations were compared with a few previous governing equations. The comparisons show that proposed equations are with higher precision. Besides, the proposed equations can be viewed as the asymptotic governing equations of Lagrange’s equations of motion for large displacement. Finally, the corresponding boundary conditions and the comparison between the presented model equation and classical model equation were provided.

Internal resonance of an axially transporting beam with a two-frequency parametric excitation

“…Based on the Galerkin scheme and direct timeintegration, the three-dimensional nonlinear global dynamics of an axially moving viscoelastic beam was carried out by Farokhi et al [13] . The kinematic aspects in modeling large-amplitude vibration of an axially moving beam were formulated in the mixed Eulerian-Lagrangian framework by Wang et al [14] . Considering the effects of structural damping and axially moving, Ding et al [15] studied the effects of the parameters on unstable regions and response curves.…”