On Internal Resonance of Nonlinear Nonuniform Beams

This paper reports the case of internal resonance three-to-one with frequency of excitation near natural frequency in the case of bending vibrations of nonuniform cantilever with small damping. The case of nonlinear curvature, moderately large amplitudes, is considered. The method of multiple scales is applied directly to the nonlinear partial-differential equation of motion and boundary conditions. The phase-amplitude equations are analytically determined. Steady-state response is reported.