Abstract
The effect of an open edge crack on the parameters of an isotropic aluminum cantilever beam was investigated. The rotational stiffness and flexibility of the cantilever beam crack were analytically calculated for various crack depths. The results showed that as the depth of the crack increased, the rotational stiffness decreased and flexibility increased. For the intact cantilever beam, acceptable variation was validated by comparing the analytically estimated natural frequencies of the first three modes of bending vibration, and those obtained through modal analysis using the block Lanczos method of finite element analysis software ANSYS v16. The software was used to perform a structural, modal and harmonic analysis of the cracked cantilever beam under different scenarios. The results showed a reduction in the natural frequencies with the existence of the crack. The amount of the reduction varied based on the location and depth of the crack and the pattern of mode shapes. The calculated value of stiffness of the cantilever beam decreased with the presence of the crack. The amount of the decrease was dependent on the depth and location of the crack. The calculated values of the (SIF) stress intensity factor in mode I of the crack (opening edge crack) were proportional to the depth of the crack and inversely proportional to the distance of the crack from the fixed end of the cantilever beam. Based on these results, it is inferred that changes in the modal and structural parameters of the cracked cantilever beam were evidence which could be used to identify cracks.
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M. Behzad, A. Meghdari, A. Ebrahimi, A new approach for vibration analysis of a cracked beam. Int. J. Eng. Trans. B Appl. 18(4), 319–330 (2005)
M. Heydari, A. Ebrahimi, M. Behzad, Forced vibration analysis of a Timoshenko cracked beam using a continuous model for the crack. Eng. Sci. Technol. Int. J. 17(4), 194–204 (2014)
S. Choudhury, D.N. Thatoi, K. Maity, S. Sau, M.D. Rao, A modified support vector regression approach for failure analysis in beam-like structures. J. Fail. Anal. Prev. 18(4), 998–1009 (2018)
D.K. Agarwalla, D.R. Parhi, Effect of crack on modal parameters of a cantilever beam subjected to vibration, in Chemical, Civil and Mechanical Engineering Tracks of 3rd Nirma University International Conference on Engineering. (Ahmedabad, India, 2012), Procedia Engineering, 2013, vol. 51, pp. 665–669
A. Banerjee, G. Pohit, Crack investigation of rotating cantilever beam by fractal dimension analysis, in 2nd International Conference on Innovations in Automation and Mechatronics Engineering. (Vallabh Vidyanagar, India, 2014), Procedia Technology, 2014, vol. 14, pp. 188–195
I.A. Khan, D.R. Parhi, Finite element analysis of double cracked beam and its experimental validation, in Chemical, Civil and Mechanical Engineering Tracks of 3rd Nirma University International Conference on Engineering. (Ahmedabad, India, 2012), Procedia Engineering, 2013, vol. 51, pp. 703–708
J. Liu, W.D. Zhu et al., A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips. J. Sound Vib. 382, 274–290 (2016)
J. Zeng, H. Ma, W. Zhang, B. Wen, Dynamic characteristic analysis of cracked cantilever beams under different crack types. Eng. Fail. Anal. 74, 80–94 (2017)
M.S. Mia, M.S. Islam, U. Ghosh, Modal analysis of cracked cantilever beam by finite element simulation, in 10th International Conference on Marine Technology. (Dhaka, Bangladesh, 2016), Procedia Engineering, 2017, vol. 194, pp. 509–516
B.P. Nandwana, S.K. Maiti, Modelling of vibration of beam in presence of inclined edge or internal crack for its possible detection based on frequency measurements. Eng. Fract. Mech. 58(3), 193–205 (1997)
V.R. Khalkar, S. Ramachandran, Study of free undamped and damped vibrations of a cracked cantilever beam. J. Eng. Sci. Technol. 13(2), 449–462 (2018)
A.K. Batabyal, P. Sankar, T.K. Paul, Crack detection in cantilever beam using vibration response. ed by E. Inan et al. Vibration Problems ICOVP-2007. Springer Proc. Phys. vol. 126, pp. 27–33 (2008)
M. Djidrov, V. Gavriloski, J. Jovanova, Vibration analysis of cantilever beam for damage detection. FME Trans. 42, 311–316 (2014)
R.K. Behera, A. Pandey, D.R. Parhi, Numerical and experimental verification of a method for prognosis of inclined edge crack in cantilever beam based on synthesis of mode shapes, in 2nd International Conference on Innovations in Automation and Mechatronics Engineering. (Vallabh Vidyanagar, India, 2014), Procedia Technology, 2014, vol. 14, pp. 67–74
A. Cicirello, A. Palmeri, Static analysis of Euler–Bernoulli beams with multiple unilateral cracks under combined axial and transverse loads. Int. J. Solids Struct. 51(5), 1020–1029 (2014)
M.J. Mungla, D.S. Sharma, R.R. Trivedi, Identification of a crack in clamped-clamped beam using frequency-based method and genetic algorithm, in 12th International Conference on Vibration Problems, ICOVP. (Guwahati, India, 2015), Procedia Engineering, 2016, vol. 144, pp. 1426–1434
A.D. Dimarogonas, S.A. Paipetis, Analytical Methods in Rotor Dynamics (Elsevier, London, 1983)
P.F. Rizos, N. Aspragathos, A.D. Dimarogonas, Identification of crack location and magnitude in a cantilever beam from the vibration modes. J. Sound Vib. 138(3), 381–388 (1990)
K.H. Barad, D.S. Sharma, V. Vyas, Crack detection in cantilever beam by frequency based method, in Chemical, Civil and Mechanical Engineering Tracks of 3rd Nirma University International Conference on Engineering. (Ahmedabad, India, 2012), Procedia Engineering, 2013, vol. 51, pp. 770–775
A.J. Dentsoras, A.D. Dimarogonas, Resonance controlled fatigue crack propagation in a beam under longitudinal vibrations. Int. J. Fract. 23(1), 15–22 (1983)
W.M. Ostachowicz, M. Krawczuk, Analysis of the effect of cracks on the natural frequencies of a cantilever beam. J. Sound Vib. 150(2), 191–201 (1991)
Y. Nakasone, S. Yoshimoto, T.A. Stolarski, Engineering Analysis Using ANSYS Software (Elsevier Butterworth-Heinemann, Oxford, 2006)
M.A.B. Marzuki, M.H.A. Halim, A.R.N. Mohamed, Determination of natural frequencies through modal and harmonic analysis of space frame race car chassis based on ANSYS. Am. J. Eng. Appl. Sci. 8(4), 538–548 (2015)
V. Khalkar, S. Ramachandran, Free vibration study of v-shape and rectangular shape double-sided cracks in a cantilever beam. J. VibroEng. 19(2), 1026–1038 (2017)
E.S.M.M. Soliman, Static and vibration analysis of CFRP composite mono leaf spring. J. Fail. Anal. Prev. 19(1), 5–14 (2019)
M.V.M.O. Filho et al., Analysis of sensor placement in beams for crack identification. Lat. Am. J. Solids Struct. 15(11), 1–18 (2018)
M. Romaszko, B. Sapinski, A. Sioma, Forced vibrations analysis of a cantilever beam using the vision method. J. Theor. Appl. Mech. 53(1), 243–254 (2015)
V. Khalkar, S. Ramachandran, The effect of crack geometry on stiffness of spring steel cantilever beam. J. Low Freq. Noise Vib. Act. Control. 0, 1–13 (2018)
H. Ma, J. Zeng et al., Analysis of the dynamic characteristics of a slant-cracked cantilever beam. Mech. Syst. Signal Process. 75, 261–279 (2016)
N. Perez, Fracture Mechanics (Kluwer Academic Publishers, Boston, 2004)
R. Shao, F. Dong et al., Influence of cracks on dynamic characteristics and stress intensity factor of gears. Eng. Fail. Anal. 32, 63–80 (2013)
R.G. Ahangar, Y. Verreman, Assessment of mode I and mode II stress intensity factors obtained by displacement extrapolation and interaction integral methods. J. Fail. Anal. Prev. 19(1), 85–97 (2019)
Y. Liao, Y. Li et al., Residual fatigue life analysis of cracked aluminum lithium alloy plates repaired with titanium alloy patches for different sizes. J. Fail. Anal. Prev. 19(1), 258–269 (2019)
V. Sivakumar, K.P. Dani, S. Sriram, Prediction of stress intensity factor on precracked composite wing rib made up of carbon-epoxy IM7-8552. J. Fail. Anal. Prev. 16(4), 635–646 (2016)
A.Y.T. Leung, Z. Zhou, X. Xu, Determination of stress intensity factors by the finite element discretized symplectic method. Int. J. Solids Struct. 51(5), 1115–1122 (2014)
S.J. Rouzegar, M. Mirzaei, Modeling dynamic fracture in Kirchhoff plates and shells using the extended finite element method. Sci. Iran. 20(1), 120–130 (2013)
J. Wang, X.Q. Zhang et al., Investigation of fatigue growth behavior of an inclined crack in aluminum alloy plate. J. Fail. Anal. Prev. 18(5), 1159–1167 (2018)
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Soliman, E.S.M.M. Investigation of Crack Effects on Isotropic Cantilever Beam. J Fail. Anal. and Preven. 19, 1866–1884 (2019). https://doi.org/10.1007/s11668-019-00796-7
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DOI: https://doi.org/10.1007/s11668-019-00796-7