504
G.-R. Gillich et al.
4 Conclusion
In the current study, we have plotted the PSC for a steel beam having one transversal
crack of known dimensions and position, by employing an original relation that
considers the RFS and the SNMC.
It was found that the intersection of the plotted PSC indicates precisely the damage
location of all presented cases.
In the particular case where the beams end constraints are fixed-fixed, it was
found that the PSC indicates two symmetric positioned damages, and this is due to
the modal curvature symmetry caused by the constraint, showing that for this case it
is enough to employ only half of the calculated severity values for locating the crack.
The study shows that the PSC algorithm is a very precise method for detecting,
evaluating and locating damages in beam-like structures.
References
1. E. Mesquita, P. Antunes, F. Coelho, P. André, A. Arêde, H. Varum, Global overview on advances
in structural health monitoring platforms. J. Civ. Struct. Health Monit. 6(3), 461–475 (2016)
2. Z.B. Yang, M. Radzienski, P. Kudela, W. Ostachowicz, Damage detection in beam-like composite
structures via Chebyshev pseudo spectral modal curvature. Compos. Struct. 168, 1–12 (2017)
3. S. Khatir, K. Dekemele, M. Loccufier, T. Khatir, M.A. Wahab, Crack identification method in
beam-like structures using changes in experimentally measured frequencies and Particle Swarm
Optimization. C. R. Mec. 346(2), 110–120 (2018)
4. R. Zenzen, I. Belaidi, S. Khatir, M.A. Wahab, A damage identification technique for beam-like
and truss structures based on FRF and Bat Algorithm. C. R. Mec. 346(12), 1253–1266 (2018)
5. M.H. He, T. Yang, Y. Du, Nondestructive identification of composite beams damage based on
the curvature mode difference. Compos. Struct. 176, 178–186 (2017)
6. J.T. Ravi, S. Nidhan, N. Muthu, S.K. Maiti, Analytical and experimental studies on detection
of longitudinal, L and inverted T cracks in isotropic and bi-material beams based on changes in
natural frequencies. Mech. Syst. Signal Process. 101, 67–96 (2018)
7. G.R. Gillich, Z.I. Praisach, Modal identification and damage detection in beam-like structures
using the power spectrum and time–frequency analysis. Signal Processing. 96(A), 29–44 (2014)
8. Z.I. Praisach, G.R. Gillich, C. Protocsil, F. Muntean, Evaluation of crack depth in beams for
known damage location based on vibration modes analysis. Appl. Mech. Mater. 430, 90–94
(2013)
9. M. Dahak, N. Touat, M. Kharoubi, Damage detection in beam through change in measured
frequency and undamaged curvature mode shape. Inverse Prob. Sci. Eng. 27, 89–114 (2019)
G.-R. Gillich et al.
4 Conclusion
In the current study, we have plotted the PSC for a steel beam having one transversal
crack of known dimensions and position, by employing an original relation that
considers the RFS and the SNMC.
It was found that the intersection of the plotted PSC indicates precisely the damage
location of all presented cases.
In the particular case where the beams end constraints are fixed-fixed, it was
found that the PSC indicates two symmetric positioned damages, and this is due to
the modal curvature symmetry caused by the constraint, showing that for this case it
is enough to employ only half of the calculated severity values for locating the crack.
The study shows that the PSC algorithm is a very precise method for detecting,
evaluating and locating damages in beam-like structures.
References
1. E. Mesquita, P. Antunes, F. Coelho, P. André, A. Arêde, H. Varum, Global overview on advances
in structural health monitoring platforms. J. Civ. Struct. Health Monit. 6(3), 461–475 (2016)
2. Z.B. Yang, M. Radzienski, P. Kudela, W. Ostachowicz, Damage detection in beam-like composite
structures via Chebyshev pseudo spectral modal curvature. Compos. Struct. 168, 1–12 (2017)
3. S. Khatir, K. Dekemele, M. Loccufier, T. Khatir, M.A. Wahab, Crack identification method in
beam-like structures using changes in experimentally measured frequencies and Particle Swarm
Optimization. C. R. Mec. 346(2), 110–120 (2018)
4. R. Zenzen, I. Belaidi, S. Khatir, M.A. Wahab, A damage identification technique for beam-like
and truss structures based on FRF and Bat Algorithm. C. R. Mec. 346(12), 1253–1266 (2018)
5. M.H. He, T. Yang, Y. Du, Nondestructive identification of composite beams damage based on
the curvature mode difference. Compos. Struct. 176, 178–186 (2017)
6. J.T. Ravi, S. Nidhan, N. Muthu, S.K. Maiti, Analytical and experimental studies on detection
of longitudinal, L and inverted T cracks in isotropic and bi-material beams based on changes in
natural frequencies. Mech. Syst. Signal Process. 101, 67–96 (2018)
7. G.R. Gillich, Z.I. Praisach, Modal identification and damage detection in beam-like structures
using the power spectrum and time–frequency analysis. Signal Processing. 96(A), 29–44 (2014)
8. Z.I. Praisach, G.R. Gillich, C. Protocsil, F. Muntean, Evaluation of crack depth in beams for
known damage location based on vibration modes analysis. Appl. Mech. Mater. 430, 90–94
(2013)
9. M. Dahak, N. Touat, M. Kharoubi, Damage detection in beam through change in measured
frequency and undamaged curvature mode shape. Inverse Prob. Sci. Eng. 27, 89–114 (2019)