Subharmonic and ultra-subharmonic response of nonlinear elastic beams subjected to harmonic excitation

In this paper, the dynamics response of beams subjected to transverse harmonic excitation is studied. The nonlinearity of constitutive relations of the beam material is considered. When the buckled beams compressed by axial forces are subjected to transverse period perturbation, the harmonic bifurcates into subharmonic and ultra_subharmonic sequences. The critical conditions for subharmonic and ultra_subharmonic orbits are determined by use of Melnikov method.