Vibrations of Beams in the Elasto-Plastic and Geometrically Nonlinear Regime

Abstract

This chapter presents models for beams vibrating withmoderately large displacements and with elasto - plasticity. Thebeams are initially straight, homogeneous and isotropic, and oscillatealways in one plane. A method to solve the equations ofmotion in the time domain, with computation of plastic strains in amixed hardening situation, is described. Forced oscillations underharmonic excitations are analysed using this method. A frequencydomain procedure to analyse free vibrations with existing plasticstrains is also introduced. Free vibration oscillations are then analysed,with particular attention to the combined influence of largedisplacements, i.e., geometrical nonlinearity, and plastic strains onthe shapes assumed during the period of vibration and on the naturalfrequencies.