Non-linear resonance vibrations of cracked beams in condition of driving force parameters variation

A closing crack causes the dynamic behavior of a vibrating system to be significantly non-linear and, consequently, the appearance of non-linear resonances. The main idea of the proposed procedure of crack location and size estimation is based on the determination of the vibration response non-linearity around the superharmonic resonance of order 2/1 and subharmonic resonance of order 1/2 at different parameters of driving force. First parameter under investigation is the point of force application. Second parameter is the level of driving force asymmetry. It is shown both numerically and experimentally that the abrupt change of the non-linearity of vibration response when driving force is applied close to the crack clearly indicates the location of crack. Addition of the static component to the harmonic driving force varies the level of the vibration response non-linearity at any non-linear resonance in case of crack presence. Based on the variation of the driving force parameters the procedure of damage detection is proposed.