While structural damage detection based on flexural vibration shapes, such as mode shapes and steady-state response shapes under harmonic excitation, has been well developed, little attention is paid to that based on longitudinal vibration shapes that also contain damage information. This study originally formulates a slope vibration shape for damage detection in bars using longitudinal vibration shapes. To enhance noise robustness of the method, a slope vibration shape is transformed to a multiscale slope vibration shape in a multiscale domain using wavelet transform, which has explicit physical implication, high damage sensitivity, and noise robustness. These advantages are demonstrated in numerical cases of damaged bars, and results show that multiscale slope vibration shapes can be used for identifying and locating damage in a noisy environment. A three-dimensional (3D) scanning laser vibrometer is used to measure the longitudinal steady-state response shape of an aluminum bar with damage due to reduced cross-sectional dimensions under harmonic excitation, and results show that the method can successfully identify and locate the damage. Slopes of longitudinal vibration shapes are shown to be suitable for damage detection in bars and have potential for applications in noisy environments.
Structural Damage Detection Using Slopes of Longitudinal Vibration Shapes