Abstract
Analytical results are presented on nonlinear coupled vibrations of a post-buckled clamped beam with a tip-mass constrained by an axial spring. First, governing equations of the beam are derived including both effects of the axial inertia force and the geometrical nonlinearity of the beam. The modified Galerkin procedure is applied to the governing equation by introducing a coordinate function for the axial displacement considering the quadratic nonlinear coupling with the deflection. Nonlinear periodic responses are calculated with the harmonic balance method. Owing to the axial inertia of the tip-mass, the amplitude of the principal resonance of the beam is increased, which agrees well with the experimental results formerly presented.
