Nonlinear Transverse Vibrations of a Beam with Multiple Breathing Edge Cracks

One step beyond the studies of transverse vibration of beams with a breathing edge crack is the verification of the theoretical crack beam models with an experimental test set up. Beams with a single breathing edge crack can be used as a specimen for the experimental test. However, there is no assurance against the unexpected additional cracks in the specimens, whichmay cause unexpected results. Therefore, in this paper nonlinear transverse vibration of a beam with multiple breathing edge cracks is considered as a preliminary study. The breathing effect of the cracks are modeled as piecewise linear stiffness and a harmonic force is applied to the cracked beam. Galerkin'sMethod is applied with multiple trial functions and nonlinear differential equations obtained are solved by using harmonic balance method with multi harmonics. Utilizing the developed model, effects of crack parameters and crack locations are studied.