Damage detection in structures using angular velocity

A new methodology is presented in this work to detect, localize, and relatively quantify damage in structures based on the changes in the second spatial derivative (curvature) of the power spectral density (PSD) of the angular velocity during vibration. The proposed method is based on the output motion only and does not require information about the input forces/motions. The PSD of the angular velocity signal at different locations on structural beams was used to identify the frequencies where the beams show large angular velocity. The curvature of the PSD of the angular velocity at these peak frequencies was then calculated. A damage index is presented that measures the differences between the PSD curvature of the angular velocity of a damaged structure and an artificial healthy baseline structure. The efficacy of the proposed method in detecting and localizing single and multiple damages was numerically demonstrated on structural beams with the presence of white noise. The method was very effective in detecting and localizing small damage on beams with narrow slots even when 10% white noise was added to the measured data. The method also successfully detected and localized a narrow slot in laboratory testing of a cantilever beam.