Modal asymptotic analysis of sub-harmonic and quasi-periodic flexural vibrations of beams with cracks

Abstract

Nonlinear finite-DOF dynamical system is derived to describe the beam vibrations with transversal crack. The beam deflections are expanded by using the eigenmodes and contact parameter. The Galerkin method is applied to the partial differential equation, which describes the structure vibrations. Two- and three-DOF nonlinear dynamical systems with internal resonance are analyzed. The multiple scales method is used to investigate both the principle second resonance and the combination one. The resonance quasi-periodic and sub-harmonic motions are analyzed. The quasi-periodic motions are arisen due to the Neimark–Sacker bifurcation.