Damage Detection of Axially Loaded Beam: A Frequency-Based Method

Document Type: Technical Notes

Authors

1 Assistant Professor of Civil Engineering Department, Research Institute of Advanced Technology in Civil Engineering, Semnan University, Semnan, Iran.

2 M.Sc, Research Institute of Advanced Technology in Civil Engineering, Semnan University, Semnan, Iran.

Abstract

The present study utilizes an analytical method to formulate the three lowest modal frequencies of axially-loaded notched beam through both crack location and load level in a specific format that can be used in existing frequency-based crack-identification methods. The proposed formula provides a basis to shift into two states, one with axial loading and the other without any loading whatsoever. When any two natural frequencies in simply-supported beam with an open crack, subjected to axial load, are measured, crack position and extent can be determined, using a characteristic equation, which is a function of crack location, sectional flexibility, and eigenvalue (natural frequency). Theoretical results show high accuracy for service axial loads. In this range, errors for crack location and extent are less than 12% and 10%, respectively.

Keywords

Main Subjects


Attar, M. (2012). "A transfer matrix method for free vibration analysis and crack identification of stepped beams with multiple edge cracks and different boundary conditions", International Journal of Mechanical Sciences, 57(1), 19-33.
Bakhtiari-Nejad, F, Khorram, A. and Rezaeian, M. (2014). "Analytical estimation of natural frequencies and mode shapes of a beam having two cracks", International Journal of Mechanical Sciences, 78, 193-202.
Binici, B. (2005). "Vibration of beams with multiple open cracks subjected to axial force", Journal of Sound and Vibration, 287(1-2), 277-295.
Caddemi, S. and Calio, I. (2009). "Exact closed-form solution for the vibration modes of the Euler-Bernouli beam with multiple open cracks", Journal of Sound and Vibration, 327(3-5), 473-489.
Cicirello, A. and Palmeri, A. (2014). "Static analysis of Euler–Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads",International Journal of Solids and Structures, 51(5), 1020-1029.
Gomes, H.M. and Almeida, F.J.J. (2014). "An analytical dynamic model for single-cracked beams including bending, axial stiffness, rotational inertia, shear deformation and coupling effects", Applied Mathematical Modelling, 38(3), 938-948.
Jassim, Z.A., Ali, N.N., Mustapha, F. and Abdul-Jalil, N.A. (2013). "A review on the vibration analysis for a damage occurrence of a cantilever beam", Engineering Failure Analysis, 31, 442-461.
Khiem, N.T. (2006). "Damage detection of beam by natural frequencies: General theory and procedure", Vietnam Journal of Mechanics, VAST, 28(2), 120-132.
Khiem, N.T. and Toan, L.K. (2014). "A novel method for crack detection in beam-like structures by measurements of natural frequencies", Journal of Sound and Vibration, 333(18), 4084-4103.
Kisa, M. and Gurel, M.A. (2007). "Free vibration analysis of uniform and stepped cracked beams with circular cross sections", International Journal of Engineering Science, 45(2-8), 364-380.
Labib, A., Kennedy, D. and Featherston, C. (2014). "Free vibration analysis of beams and frames with multiple cracks for damage detection", Journal of Sound and Vibration, 333(20), 4991-5003.
Lele, S.P. and Maiti, S.K. (2002). "Modeling of transverse vibration of short beams for crack detection and measurement of crack extension", Journal of Sound and Vibration, 257(3), 559-583.
Lin, H.P. (2004). "Direct and inverse methods on free vibration analysis of simply supported beams with a crack", Engineering Structures, 26(4), 427-436.
Mazanoglu, M. and Sabuncu, M. (2012). "A frequency based algorithm for identification of single and double cracked beams via a statistical approach used in experiment", Mechanical Systems and Signal Processing, 30, 168-185.
Mazanoglu, K., Yesilyurt, I. and Sabuncu, M. (2009). "Vibration analysis of multiple-cracked non-uniform beams", Journal of Sound and Vibration, 320(4-5), 977-989.
Mei, C., Karpenko, Y., Moody, S. and Allen, D. (2006). "Analytical approach to free and forced vibrations of axially loaded cracked Timoshenko beams", Journal of Sound and Vibration, 291(3-5), 1041-1060.
Moradi, S. and Jamshidi Moghadam, P. (2014). "Vibration analysis of cracked post-buckled beams", Applied Mathematical Modelling, 38(13), 3281-3294.
Orhan, S. (2007). "Analysis of free and forced vibration of a cracked cantilever beam", NDT and E International, 40(6), 443-450.
Rizos, P.F., Aspragathos, N. and Dimarogonas, A.D. (1990). "Identification of crack location and magnitude in a cantilever beam from the vibrating mode", Journal of Sound and Vibration, 138(3), 381-388.
Saavedra, P.N. and Cuitino, L.A. (2001). "Crack detection and vibration behavior of cracked beams", Computers and Structures, 79(16), 1451-1459.
Sinha, J.K. and Friswell, M.I. (2002). "Simulation of the dynamic response of a cracked beam", Computers and structures, 80(18-19), 1473-1476.
Viola, E., Ricci, P. and Aliabadi, M.H. (2007). "Free vibration analysis of axially loaded Timoshenko beam structures using the dynamic stiffness method", Journal of Sound and Vibration, 304(1-2), 124-153.
Zheng, D.Y. and Kessissoglou, N.J. (2004). "Free vibration analysis of a cracked beam by finite element method", Journal of Sound and Vibration, 273(3), 457-475.
Zheng, T. and Ji, T. (2012). "An approximate method for determining the static deflection and natural frequency of a cracked beam", Journal of Sound and Vibration, 331(11), 2654-2670.