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Damage Detection on a Beam with Multiple Cracks: A Simplified Method Based on Relative Frequency Shifts.

Gilbert-Rainer Gillich1, Nuno M M Maia2, Magd Abdel Wahab3,4

  • 1Department of Engineering Sciences, University "Babes-Bolyai" of Cluj-Napoca, Traian Vuia Square, No. 1-4, 320085 Resita, Romania.

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Summary

This study introduces a method to detect multiple cracks in structures using relative frequency shifts (RFS). The approach accurately locates and assesses crack severity by analyzing changes in eigenfrequencies, proving reliable through experiments.

Keywords:
damage detection: multi-cracked beamdeflectioneigenfrequencysuperposition

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Area of Science:

  • Structural Health Monitoring
  • Mechanical Engineering
  • Vibrational Analysis

Background:

  • Early detection of cracks in engineering structures is crucial for preventing catastrophic failures.
  • Modal parameter analysis, particularly eigenfrequency shifts, offers advantages for damage detection.
  • Previous work established relative frequency shifts (RFS) to indicate single crack position and depth.

Purpose of the Study:

  • To extend the RFS method for detecting multiple cracks in beams.
  • To investigate the applicability of the superposition principle for multiple crack scenarios.
  • To establish a reliable benchmark for characterizing damage using eigenfrequencies.

Main Methods:

  • Developing a mathematical relation for RFS based on modal curvatures and deflections.
  • Applying the superposition principle to calculate RFS for multiple cracks.
  • Analyzing the impact of crack proximity and orientation on RFS.
  • Formulating crack assessment as an optimization problem using RFS curves.

Main Results:

  • The superposition principle is applicable for RFS calculation when cracks are sufficiently separated.
  • Cracks on the same face result in a smaller frequency drop than the sum of individual drops.
  • Cracks on opposite faces lead to a larger frequency drop than the sum of individual drops.
  • Experimental validation confirmed the accurate location and severity estimation of multiple cracks.

Conclusions:

  • The RFS method, utilizing only eigenfrequencies, provides a reliable benchmark for damage characterization.
  • The proposed approach enables accurate detection and assessment of multiple crack damage in structures.
  • This method enhances the capability of structural health monitoring systems.