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

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.