Identification of crack location and magnitude in a cantilever beam from the vibration modes

Suppression of the dynamic response of cracked beams with active control

“…The linear spring models have been successfully applied in transverse cracks beams with conditions to simulate cracks by Mohammad [2]. Rizos et al [3] employed the measured vibration modes to identify the crack locations, depths, and vibration frequencies in order to obtain the dynamic response of cracked beams. Narkis [4] employed the variation of the first two natural frequencies to obtain the locations of the cracks in the simply supported beam.…”

Damage Detections in Nonlinear Vibrating Thermally Loaded Plates

“…Thermal loads introduce stresses due to thermal expansion, which lead to changes in the modal properties. Thermal loads can also cause buckling and in some cases even lead to chaotic behaviour [1][2][3][4][5].…”

Damage detection of beam by natural frequencies: General theory and procedure

“…Then transverse (rotational) model of damage has been developed and validated by a general theory of damaged beams [3] that makes it be possible to determine the stiffness of the equivalent spring as a function of damage depth. Using the transverse model of damage Rizos et al [4] have constructed the frequency equation for cantilever beam. Narkis [5] has given the equations for simply supported beam in both the cases of transverse and axial models.…”

“…However, the question as influence of the model error (boundary conditions) and measurement noise on accuracy of the damage location has been still unanswered . The model updating problem before the damage detection is firstly investigated by Adams et al in [4] who proposed to correct the Young's modulus E as a model parameter to be updated. Moreover, the seeking intersection of curves in presence of the inaccurate model and the measurement error will be very difficult, not yet taking into account the effect of computational error.…”

“…Introducmg the parameters a = L (pA/ EI) 4 and A = a...;W, where w -natural frequency of the beam, the mode shape of vibration can be determined by the equation…”