References
- Virgin LN, Santillan ST, Holland DB. Effect of gravity on the vibration of vertical cantilevers. Mech Res Commun. 2007;34(3):312–317.
- Xi L-Y, Li X-F, Tang G-J. Free vibration of standing and hanging gravity-loaded rayleigh cantilevers. Int J Mech Sci. 2013;66:233–238.
- Yokoyama T. Vibrations of a hanging timoshenko beam under gravity. J Sound Vibr. 1990;141(2):245–258.
- Lajimi SAM, Heppler GR. Free vibration and buckling of cantilever beams under linearly varying axial load carrying an eccentric end rigid body. Trans Can Soc Mech Eng. 2013;37(1):89–110.
- Hijmissen JW, Van Horssen WT. On transverse vibrations of a vertical Timoshenko beam. J Sound Vibr. 2008;314(1–2):161–179.
- Schafer BE, Holzach H. Experimental research on flexible beam modal control. J Guidance Control Dyn. 1985;8(5):597–604.
- Jones JW, Nickell RE, Bulat W. “The effects of gravity on structural vibration.” Pressure Vessels and Piping Conference. Vol. 55744. American Society of Mechanical Engineers, 2013. 10.1115/PVP2013-97571.
- Chang JR, Lin W-J, Huang C-J, et al. Vibration and stability of an axially moving Rayleigh beam. Appl Math Modell. 2010;34(6):1482–1497. DOI:10.1016/j.apm.2009.08.022
- Panigrahi B, Pohit G. Nonlinear modelling and dynamic analysis of cracked Timoshenko functionally graded beams based on neutral surface approach. Proc Inst Mech Eng Part C J Mech Eng Sci. 2016;230(9):1486–1497.
- Loya JA, Rubio L, Fernández-Sáez J. Natural frequencies for bending vibrations of Timoshenko cracked beams. J Sound Vibr. 2006;290(3–5):640–653.
- Kharazan M, Irani S, Noorian MA, et al. Nonlinear vibration analysis of a cantilever beam with multiple breathing edge cracks. Int J Non Linear Mech. 2021;136:103774.
- Zhao X, Zhao YR, Gao XZ, et al. Green׳ s functions for the forced vibrations of cracked euler–Bernoulli beams. Mech Syst Signal Process. 2016;68:155–175.
- Viola E, Ricci P, Aliabadi MH. Free vibration analysis of axially loaded cracked timoshenko beam structures using the dynamic stiffness method. J Sound Vibr. 2007;304(1–2):124–153.
- Shankar KA, Pandey M. Nonlinear dynamic analysis of cracked cantilever beam using reduced order model. Procedia Eng. 2016;144:1459–1468.
- Yokoyama T, Chen M-C. Vibration analysis of edge-cracked beams using a line-spring model. Eng Fract Mech. 1998;59(3):403–409.
- Krawczuk M, Palacz M, Ostachowicz W. The dynamic analysis of a cracked Timoshenko beam by the spectral element method. J Sound Vibr. 2003;264(5):1139–1153.
- Kitipornchai S, Liao-Liang K, Yang J, et al. Nonlinear vibration of edge cracked functionally graded timoshenko beams. J Sound Vibr. 2009;324(3–5):962–982.
- Collini L, Garziera R, Riabova K. Detection of cracks in axially loaded tie-rods by vibration analysis. Case Stud NondestrTest Eval. 2020;35(2):121–138.
- Altunışık AC, Yesevi Okur F, Kahya V. Modal parameter identification and vibration based damage detection of a multiple cracked cantilever beam. Eng Fail Anal. 2017;79:154–170.
- Liu W, Barkey ME. Nonlinear vibrational response of a single edge cracked beam. J Mech Sci Technol. 2017;31(11):5231–5243.
- Soliman ESMM. Investigation of crack effects on isotropic cantilever beam. J Fail Anal Prev. 2019;19(6):1866–1884.
- Nikolić A, Šalinić S. Free vibration analysis of cracked beams by using rigid segment method. Appl Math Modell. 2020;84:158–172.
- Loya JA, Aranda-Ruiz J, Zaera R. Natural frequencies of vibration in cracked timoshenko beams within an elastic medium. Theor Appl Fract Mech. 2022;118:103257.
- Chen XF, He ZJ, Xiang JW. Experiments on crack identification in cantilever beams. Exp Mech. 2005;45(3):295–300.