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The attempts to identify damping changes in a cracked beam can improve the accuracy of the nonlinear crack identification method. For the purpose of this aim, a parametric nonlinear equation of motion is obtained using the Euler–Bernoulli beam theory and parametric nonlinear breathing crack assumptions. Several experiments were conducted to identify the effect of breathing cracks on changing the damping value in nonlinear vibrations of a cracked beam. Experimental tests have revealed that increasing the crack depth and the level of excitation enlarges the damping coefficient in a vibrating beam. For this reason, the effects of the excitation force and crack depth on the structural damping coefficient are investigated. The obtained results indicated that considering the nonlinear response of a cracked beam and measuring the value of the damping changes can significantly improve the accuracy of the nonlinear crack identification method. [ABSTRACT FROM AUTHOR]

The nonlinear vibration analysis of cracked structures could be a suitable indicator for diagnosing defects. When breathing cracks appear on the beam, its behavior can be modeled as a bilinear oscillator. In this paper, the nonlinear vibration behavior of a cantilever beam with multiple breathing cracks is investigated. For this purpose, the multi-cracked beam's stiffness is calculated by introducing the effective length for the local stiffness reduction in the vicinity of cracks. Furthermore, owing to the importance of the damping variation in a cracked beam, its exact value is evaluated through theoretical expressions. A continuous polynomial function with the Weierstrass approximation is exploited to simulate the bilinear behavior of breathing cracks. By performing nonlinear analysis using the perturbation technique, the cracked beam's dynamic behavior is studied. Moreover, the sensitivity of the response to the crack parameters in the primary resonance of the structure is analyzed. Finally, the sensitivity of the beam's nonlinear response to the different number of breathing cracks and various crack depths is investigated. It is shown that the beam with a higher number of cracks or deeper ones has obvious softening behavior, and hence a more significant jumping can appear in the response. [ABSTRACT FROM AUTHOR]