Modal data-based breathing crack localization in beam-column structures subjected toaxial and transverse harmonic loading

Subject Areas : Structural Mechanics

Payam Mirzaii ¹ , Fahimeh Akhlaghi ² , M Bozorgnsab ³ , Reza Taghipour ⁴ , Omid Yazdanpanah ⁵

1 -
2 -
3 - Department of Civil Engineering, Faculty of Engineering and Technology, University of Mazandaran, Babolsar, Iran
4 - Department of Civil Engineering, University of Mazandaran, Babolsar, Mazandaran, Iran
5 -

Received: 2023-07-24 Accepted : 2024-09-06 Published : 2024-09-24

Keywords: Breathing crack, Damage identification, Beam-column structures, Harmonic load, Damage index,

Abstract :

A sensitive modal data-based damage indicator is proposed to diagnose breathing cracks in beam-column structures subjected to axial load, as a percent of its critical value, and transverse harmonic load. The Newmark-Beta method is utilized to solve the equation of structural vibration, based on finite element method. The effect of Rayleigh-type damping is also examined. The indicator uses the modal deformations and their derivatives in healthy and damaged beam-column structures to identify the exact damage locations. The influence of some parameters such as noise effects and various axial loads on the efficiency of the method was also investigated. The results show the reliability of the approach in identifying the damage location for different scenarios, even in the presence of noise effect. Increasing the axial load, especially for values near to the critical load value, causes negative effects on the modal responses and their derivatives which are appropriately considered by the proposed index.

References:

1. Adams R, Cawley P, Pye C, Stone B. A vibration technique for non-destructively assessing the integrity of structures. Journal of mechanical engineering science. 1978;20(2):93-100.
2. Rizos P, Aspragathos N, Dimarogonas A. Identification of crack location and magnitude in a cantilever beam from the vibration modes. Journal of sound and vibration. 1990;138(3):381-8.
3. Pandey A, Biswas M. Damage detection in structures using changes in flexibility. Journal of sound and vibration. 1994;169(1):3-17.
4. Capecchi D, Vestroni F. Monitoring of structural systems by using frequency data. Earthquake engineering & structural dynamics. 1999;28(5):447-61.
5. Vestroni F, Capecchi D. Damage detection in beam structures based on frequency measurements. Journal of engineering mechanics. 2000;126(7):761-8.
6. Seyedpoor S, Yazdanpanah O. An efficient indicator for structural damage localization using the change of strain energy based on static noisy data. Applied Mathematical Modelling. 2014;38(9-10):2661-72.
7. Chen H-P, Bicanic N. Assessment of damage in continuum structures based on incomplete modal information. Computers & structures. 2000;74(5):559-70.
8. Yazdanpanah O, Seyedpoor S, Akbarzadeh Bengar H. A new damage detection indicator for beams based on mode shape data. Structural Engineering and Mechanics. 2015;53(4):725-44.
9. Seyedpoor S, Yazdanpanah O. Structural damage detection by differential evolution as a global optimization algorithm. Iranian Journal of Structural Engineering. 2015;1(1):52-62.
10. Karimi S, Bozorgnsab M, Taghipour R, Alipour MM. A Novel Spring-Based Model for Damage Investigation of Functionally Graded Beams. Journal of Solid Mechanics. 2021:-.
11. Taghipour R, Nashta MR, Bozorgnasab M, Mirgolbabaei H. A new index for damage identification in beam structures based on modal parameters. Archive of Mechanical Engineering. 2021;68.
12. Pai PF, Young LG. Damage detection of beams using operational deflection shapes. International journal of solids and structures. 2001;38(18):3161-92.
13. Abdo M-B, Hori M. A numerical study of structural damage detection using changes in the rotation of mode shapes. Journal of Sound and vibration. 2002;251(2):227-39.
14. Shih HW, Thambiratnam D, Chan T. Vibration based structural damage detection in flexural members using multi-criteria approach. Journal of sound and vibration. 2009;323(3-5):645-61.
15. Navabian N, Bozorgnasab M, Taghipour R, Yazdanpanah O. Damage identification in plate-like structure using mode shape derivatives. Archive of Applied Mechanics. 2016;86(5):819-30.
16. Navabian N, Taghipour R, Bozorgnasab M, Ghasemi J. Damage evaluation in plates using modal data and firefly optimisation algorithm. International Journal of Structural Engineering. 2018;9(1):50-69.
17. Moradi S, Razi P, Fatahi L. On the application of bees algorithm to the problem of crack detection of beam-type structures. Computers & Structures. 2011;89(23-24):2169-75.
18. Nobahari M, Seyedpoor SM. An efficient method for structural damage localization based on the concepts of flexibility matrix and strain energy of a structure. Structural Engineering and Mechanics. 2013;46(2):231-44.
19. Yazdanpanah O, Izadifard RA, Dehestani M. Static data based damage localization of beam-column structures considering axial load. Mechanics of Advanced Materials and Structures. 2020;27(16):1433-50.
20. Roodgar Nashta M, Taghipour R, Bozorgnasab M, Mirgolbabaei M. A novel method for identification of damage location in frame structures using a modal parameters-based indicator .Archives of Civil Engineering.2022; 68(3):633-643.
21. Ruotolo R, Surace C, Crespo P, Storer D. Harmonic analysis of the vibrations of a cantilevered beam with a closing crack. Computers & structures. 1996;61(6):1057-74.
22. Pugno N, Ruotolo R, Surace C. Analysis of the harmonic vibrations of a beam with a breathing crack. Proc 15th IMAC (Tokyo, Japan). 1997:409-13.
23. Tsyfansky S, Beresnevich V. Detection of fatigue cracks in flexible geometrically non-linear bars by vibration monitoring. Journal of Sound and vibration. 1998;213(1):159-68.
24. Tsyfansky SL, Beresnevich V. Non-linear vibration method for detection of fatigue cracks in aircraft wings. Journal of sound and vibration. 2000;236(1):49-60.
25. Guo C, Al-Shudeifat M, Yan J, Bergman L, McFarland D, Butcher E. Application of empirical mode decomposition to a Jeffcott rotor with a breathing crack. Journal of Sound and Vibration. 2013;332(16):3881-92.
26. Saavedra P, Cuitino L. Crack detection and vibration behavior of cracked beams. Computers & Structures. 2001;79(16):1451-9.
27. Bovsunovsky A, Surace C, Ruotolo R, editors. The effect of damping on the non-linear dynamic behaviour of a cracked beam at resonance and super-resonance vibrations. Key Engineering Materials; 2003: Trans Tech Publ.
28. Al-Shudeifat MA, Butcher EA. New breathing functions for the transverse breathing crack of the cracked rotor system: approach for critical and subcritical harmonic analysis. Journal of Sound and Vibration. 2011;330(3):526-44.
29. Liu W, Barkey ME. The effects of breathing behaviour on crack growth of a vibrating beam. Shock and Vibration. 2018;2018.
30. Bovsunovsky AP, Surace C. Considerations regarding superharmonic vibrations of a cracked beam and the variation in damping caused by the presence of the crack. Journal of Sound and Vibration. 2005;288(4-5):865-86.
31. Chatterjee A. Structural damage assessment in a cantilever beam with a breathing crack using higher order frequency response functions. Journal of Sound and Vibration. 2010;329(16):3325-34.
32. Joglekar D, Mitra M. Analysis of flexural wave propagation through beams with a breathing crack using wavelet spectral finite element method. Mechanical Systems and Signal Processing. 2016;76:576-91.
33. Prawin J, Lakshmi K, Rao ARM. A novel singular spectrum analysis–based baseline-free approach for fatigue-breathing crack identification. Journal of Intelligent Material Systems and Structures. 2018;29(10):2249-66.
34. Shariyat, M., Alipour, M.M. Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations. Arch Appl Mech 81, 1289–1306 (2011).
35. Chu Y, Shen M-H. Analysis of forced bilinear oscillators and the application to cracked beam dynamics. AIAA journal. 1992;30(10):2512-9.
36. Casini P, Vestroni F. Characterization of bifurcating non-linear normal modes in piecewise linear mechanical systems. International Journal of Non-Linear Mechanics. 2011;46(1):142-50.
37. Chati M, Rand R, Mukherjee S. Modal analysis of a cracked beam. Journal of sound and vibration. 1997;207(2):249-70.
38. Yoo CH, Lee S. Stability of structures: principles and applications: Elsevier; 2011.
39. Casini P, Vestroni F, Giannini O. Crack detection in beam-like structures by nonlinear harmonic identification. Frattura ed Integrità Strutturale. 2014;8(29):313-24.
40. Benfratello S, Cacciola P, Impollonia N, Masnata A, Muscolino G. Numerical and experimental verification of a technique for locating a fatigue crack on beams vibrating under Gaussian excitation. Engineering Fracture Mechanics. 2007;74(18):2992-3001.
41. Zareian F, Medina RA. A practical method for proper modeling of structural damping in inelastic plane structural systems. Computers & structures. 2010;88(1-2):45-53.
42. Haselton CB, Liel AB, Deierlein GG, Dean BS, Chou JH. Seismic collapse safety of reinforced concrete buildings. I: Assessment of ductile moment frames. Journal of Structural Engineering. 2011;137(4):481-91.
43. Chopra AK. Dynamics of structures. Theory and Application to Earthquake Engineering: Prentice Hall, New Jersey; 1995.
44. Chowdhury I, Dasgupta SP. Computation of Rayleigh damping coefficients for large systems. The Electronic Journal of Geotechnical Engineering. 2003;8(0):1-11.
45. Song Z, Su C. Computation of Rayleigh damping coefficients for the seismic analysis of a hydro-powerhouse. Shock and Vibration. 2017;2017.
46. Gavin H. Numerical integration for structural dynamics. Department of Civil and Environmental Engineering, Duke University: Durham, NC, USA2001.
47. Zhou X, Sha D, Tamma KK. A novel non‐linearly explicit second‐order accurate L‐stable methodology for finite deformation: hypoelastic/hypoelasto‐plastic structural dynamics problems. International Journal for Numerical Methods in Engineering. 2004;59(6):795-823.
48. Soroushian A, editor On practical performance of a technique recently proposed for time integration analysis with less computational cost. Proceedings of the 17th International Congress on Sound & Vibration; 2010.
49. Nateghi F, Yakhchalian M, editors. On less computational costs for analysis of silos seismic behaviors by time integration. Proceedings of the 3rd ECCOMAS thematic conference on computational methods in structural dynamics and earthquake engineering (COMPDYN 2011), Corfu; 2011.
50. MATLAB M. Statistics and Machine Learning Toolbox: 2017a–Ensemble Methods. The MathWorks Inc, Natick, Massachusetts, United States. 2017.