SUBHARMONIC RESONANCE OF AXIALLY MOVING LAMINATEED PLATES SUBJECTED TO FOLLOWER FORCES

The subharmonic resonance of the axially moving orthotropic laminated plates under follower force was investigated. Based on the kinetic energy, potential energy, mid-plane strain potential energy, the strain potential energy caused by the axial tensile force and the external virtual work, the nonlinear vibration equations of the laminated plate were derived by using the Hamiltonian principle. The dimensionless nonlinear vibration differential equations with regards to time were achieved by using the Galerkin method. The multi-scale method was used to solve differential equations of the 1/3 subharmonic resonance, and the amplitude-frequency response equations of steady-state motion for different modes were obtained. Finally, through the analysis of the examples, the characteristic curves of amplitude varying with different parameters, e.g., the tuning parameter, the velocity, the excitation amplitude, and the critical point curves for exciting double-value resonance were plotted, respectively. The results showed that the resonance amplitudes were double-valued. Moreover, the amplitudes in different modal resonance cases were obviously different.