Modal identification and damage detection in beam-like structures using the power spectrum and time–frequency analysis

• Mathematical model describing the frequency shifts for bending vibration modes.
• Method to detect damages in beams based on a continuous approach.
• Algorithm based on time–frequency analysis and power spectrum to enhance readability of frequencies.

This paper presents a new method, based on natural frequency changes, able to detect damages in beam-like structures and to assess their location and severity, considering the particular manner in which the natural frequencies of the weak-axis bending vibration modes change due to the occurrence of discontinuities. The problem is to accurately determine frequencies, because their changes present low sensitivity to damage; moreover, in some modes the damping effect is significant, and thus the analyzed signal has to be precisely identified in time. To overcome these difficulties, we propose a three-step approach. In the first stage a time–frequency analysis is performed, to roughly determine the frequency range for the first ten weak-axis bending vibration modes and to locate in time the relevant signal segment for each of the harmonics. Afterwards, filters are applied to the signal, in order to visualize the individual components corresponding to these ten vibration modes. Finally, the power spectrum of each signal component is calculated for the relevant signal segment and for integer periods of the respective harmonic. Having the precise frequencies for the healthy and damaged structure, one can calculate the frequency shifts, and thus damage location and assessment become a pattern recognition problem. It consists in comparing the measured frequency changes with values obtained analytically, using a relation which defines these changes contrived by the authors. The method's performance was experimentally proven on steel beams, for various damage scenarios and boundary conditions.