Analysis of Nonlinear Response of Cracked Beams

Based on the Lagrange’s equation, the equation of motion for pinned-pinned cracked beam with hollow section is derived. The equation of motion takes account of the geometric nonlinearity and opening and closing of the crack. Based on a numerical method, the superand sub-harmonic resonances are studied when the cracked supported pipes conveying fluid are excited by a harmonic force and the conclusions are the same as the existed researches. Then the effect of the geometric nonlinearity on response of beam with hollow section under harmonic force with large amplitude are further studied. These researches are useful for the cracks detection in the beam with hollow section.