This paper proposes a response-only method in frequency domain for structural damage detection by using the derivative of natural frequency curve of beam-like structures with a traversing auxiliary mass. The approach just uses the response time history of beam-like structures and does not need the external source of force excitation. The natural frequencies of a damaged beam with a traversing auxiliary mass change due to change in flexibility and inertia of the beam as the auxiliary mass is traversed along the beam. Therefore the auxiliary mass can enhance the effects of the crack on the dynamics of the beam and, therefore, facilitating locating the damage in the beam. That is, the auxiliary mass can be used to probe the dynamic characteristic of the beam by traversing the mass from one end of the beam to the other. However, it is impossible to obtain accurate modal frequencies by the direct operation of the Fast Fourier Transform of the response data of the structure because the frequency spectrum can be only calculated from limited sampled time data which results in the well-known leakage effect. A spectrum correction method is employed to estimate high accurate frequencies of structures with a traversing auxiliary mass. In the present work, the modal responses of damaged simply supported beams with auxiliary mass are computed using the Finite Element Analysis. The graphical plots of the natural frequencies versus axial location of auxiliary mass are obtained. The derivatives of natural frequency curve can provide crack information for damage detection of beam-like structures. However, it is suggested that the derivative do not go beyond the third derivative of natural frequency curves to avoid the difference approximation error which will be magnified at higher derivative. The sensitivity of crack index for different noise, crack depth, auxiliary mass and damping ratio are also investigated. The simulated result demonstrated the efficiency and precision of the response-only frequency-domain method which can be recommended for the real application in structural damage detection.
Damage detection of a structure based on natural frequency ratio measurements