A novel method for crack detection in beam-like structures by measurements of natural frequencies

• The Rayleigh quotient extended for multiple cracked beam allows an explicit expression of any natural frequency of the beam to be established.
• The obtained representation provides a more simple and accurate tool for calculating the arbitrary natural frequency of the multiple cracked beam.
• A novel procedure is proposed for consistent detection of unknown number of cracks by measurement only of the natural frequencies.
• Numerical and experimental results validated usefulness of the proposed method in both the direct and inverse problems for multiple cracked beam with clamped ends.

A novel method is proposed for calculating the natural frequencies of a multiple cracked beam and detecting unknown number of multiple cracks from the measured natural frequencies. First, an explicit expression of the natural frequencies through crack parameters is derived as a modification of the Rayleigh quotient for the multiple cracked beams that differ from the earlier ones by including nonlinear terms with respect to crack severity. This expression provides a simple tool for calculating the natural frequencies of the beam with arbitrary number of cracks instead of solving the complicated characteristic equation. The obtained nonlinear expression for natural frequencies in combination with the so-called crack scanning method proposed recently by the authors allowed the development of a novel procedure for consistent identification of unknown amount of cracks in the beam with a limited number of measured natural frequencies. The developed theory has been illustrated and validated by both numerical and experimental results.