This paper presents a wavelet spectrum technique for monitoring a sudden crack of a beam-like bridge structure during earthquake excitation. When there is a sudden crack caused by earthquake excitation the stiffness of the structure is changed leading to a sudden change in natural frequencies during vibration. It is difficult to monitor this sudden change in the frequency using conventional approaches such as Fourier transform because in Fourier transform the time information is lost so that it is impossible to analyse short time events. To overcome this disadvantage, wavelet spectrum, a time-frequency analysis, is used for monitoring a sudden change in frequency duringearthquake excitation for crack detection. In this study, a model of 3D crack is applied. The derivation of the stiffness matrix of a 3D cracked beam element with rectangular section adopted from fracture mechanics is presented. Numerical results showed that the sudden occurrence of the crack during earthquake excitation can be detected by the sudden change in frequency using wavelet power spectrum. When the crack depth increases, the instantaneous frequency (IF) of the structure is decreased.

ABSTRACT. The classical 3D beam element has been modified and developed as a new finite element for vibration analysis of frame structures with flexible connections and cracked mem hers. The mass and stiffness matrices of the modified elements are established basing on a new form of shape functions, which are obtained in investigating a beam with flexible supports and crack modeled through equivalent springs. These shape functions remain the cubic polynomial form and contain flexible connection (or crack) parameters. They do not change standard procedure of the finite element method (FEM). Therefore, the presented method is easy for engineers in application and allows to analyze eigen-parameters of structures as functions of the connection (or crack) parameters. The proposed approach has been applied to calculate natural frequencies and mode shape of typical frame structures in presented examples.

This paper presents the free vibration of a cracked double-beam carrying a concentrated mass located at an arbitrary position. The double-beam consisting of two different simply supported beams connected by an elastic medium is modelled by using finite element method. The influence of the concentrated mass on the frequencies and mode shapes is investigated. The relationship between the natural frequency and the location of concentrated mass is established and related to the mode shapes. The numerical simulations show that when there is a crack, the frequency of the double-beam changes sharply when the concentrated mass is located close to the crack position. This sharp change can be amplified by wavelet transform and this is useful for crack detection. The crack location can be determined by the location of peaks in the wavelet transform of the relationship between frequency and mass location.

The receptance function has been studied and applied widely since it interrelates the harmonic excitation and the response of a structure in the frequency domain. This paper presents the derivation of the exact receptance function of continuous cracked beams and its application for crack detection. The receptance curvature is defined as the second derivative of the receptance. The influence of the crack on the receptance and receptance curvature is investigated. It is concluded that when there are cracks the receptance curvature has sharp changes at the crack positions. This can be applied for the crack detection purpose. In this paper, the numerical simulations are provided.

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