ELASTIC-PLASTIC VIBRATIONS OF A BUCKLED BEAM

The paper discusses non-linear vibrations of a buckled beam under harmonic excitation. The material of the beam is elastic-plastic with linear strain-hardening. The equations of motion are integrated by Galerkin's method. The validity of the assumption, that the membrane force is constant along the beam, is discussed. It is shown that even in the case of elastic deformations, this hypothesis may cause great discrepancies in the deflection history diagrams to be compared with the real solution. In the elastic case, the Melnikov method has been used for estimating the threshold transverse load at which chaotic motion can take place. In the range of elastic-plastic vibrations, chaotic motion of the beam is discussed,