Crack identification and characterization in beams by nonlinear vibration analysis

The slight nonlinear character of a vibrating cracked beam is exploited for the purpose of determining crack location, crack depth, and crack-opening load. The approach is motivated by examining the response of a bilinear spring-mass system to excitation at two frequencies, such that the sum or difference of the two frequencies is the resonant frequency of the system. The numerically generated steady-state response of the system is used to identify the presence of the bilinear spring, even if the difference between the compressive and tensile stiffness is very small. The same idea is applied to a cracked beam forced at two frequencies, with the crack providing a local bilinear stiffness in the beam. The numerically generated steady-state response is used to identify the effect of the opening and closing of the crack. The prominence of this crack signature is then correlated with crack position and depth. It is shown that the crack signature is maximized if a static load is also placed on the beam that would cause the crack to be on the verge of opening, thus determining the crack-opening load. The dependence of the crack signature upon the system parameters and the forcing amplitudes is explored through first-order perturbation methods applied to both the bilinear spring-mass system and the cracked beam. Finally, some experimental results are presented.U of I OnlyETDs are only available to UIUC Users without author permissio