References
- Catal, S. (2006), "Analysis of free vibration of beam on elastic soil using differential transform method", Struct. Eng. Mech., 24, 51-62. https://doi.org/10.12989/sem.2006.24.1.051
- Catal, S. (2008), "Solution of free vibration equations of beam on elastic soil by using differential transform method", Appl. Math. Model., 32, 1744-1757. https://doi.org/10.1016/j.apm.2007.06.010
- Catal, S. and Catal, H.H. (2006), "Buckling analysis of partially embedded pile in elastic soil using differential transform method", Struct. Eng. Mech., 24, 24-268.
- Celebi, K., Keles, I. and Tutuncu, N. (2011), "Exact solutions for forced vibration of non-uniform rods by Laplace Transformation", Gazi University Journal of Science, 24, 347-353.
- Chen, C.K. and Ho, S.H. (1996), "Application of differential transformation to eigenvalue problem", J. Appl. Math. Comput., 79, 173-188. https://doi.org/10.1016/0096-3003(95)00253-7
- Chen, C.K. and Ho, S.H. (1999), "Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform", Int. J. Mech. Sci., 41, 1339-1356. https://doi.org/10.1016/S0020-7403(98)00095-2
- Chopra, A.K. (1995), Dynamics of Structures, Prentice-Hall Inc., New Jersey.
- Clough, R.W. and Penzien, J. (1993), Dynamics of Structures, 2nd Ed., McGraw-Hill Inc., Singapore.
- Demirdag, O. and Yesilce, Y. (2011), "Solution of free vibration equation of elastically supported Timoshenko columns with a tip mass by differential transform method", Adv. Eng. Softw., 42, 860-867. https://doi.org/10.1016/j.advengsoft.2011.06.002
- Fan, Z.J., Lee, J.H., Kang, K.H. and Kim, K.J. (1998), "The forced vibration of a beam with viscoelastic boundary supports", J. Sound Vib., 210, 673-682. https://doi.org/10.1006/jsvi.1997.1353
- Hassan, I.H.A.H. (2002a), "On solving some eigenvalue problems by using differential transformation", Appl. Math. Comput., 28, 513-525.
- Hassan, I.H.AH. (2002b), "Different applications for the differential transformation in the differential equations", Appl. Math. Comput., 129, 183-201. https://doi.org/10.1016/S0096-3003(01)00037-6
- Hilal, M.A. (2003), "Forced vibration of Euler-Bernoulli beams by means of dynamic Green functions", J. Sound Vib., 267, 191-207. https://doi.org/10.1016/S0022-460X(03)00178-0
- Jang, M.J. and Chen, C.L. (1997), "Analysis of the response of a strongly non-linear damped system using a differential transformation technique", Appl. Math. Comput., 88, 137-151. https://doi.org/10.1016/S0096-3003(96)00308-6
- Kai-yuan, Y., Xiao-hua, T. and Zhen-yi, J. (1992), "General analytic solution of dynamic response of beams with nonhomogenity and variable cross-section", Appl. Math. Mech., 13, 779-791. https://doi.org/10.1007/BF02481798
- Oniszczuk, Z. (2003), "Forced transverse vibrations of an elastically connected complex simply supported bouble-beam system", J. Sound Vib., 264, 273-286. https://doi.org/10.1016/S0022-460X(02)01166-5
- Ozgumus, O.O. and Kaya, M.O. (2006), "Flabse bending vibration analysis of rotating tapered cantilever Bernoulli- Euler beam by differential transform method", J. Sound Vib., 289, 413-420. https://doi.org/10.1016/j.jsv.2005.01.055
- Ozgumus, O.O. and Kaya, M.O. (2010), "Vibration analysis of rotating tapered Timoshenko beam by using DTM", Mechanica, 45, 33-42. https://doi.org/10.1007/s11012-009-9221-3
- Paz, M. (1997), Structural Dynamics, 4th Ed., Chapman & Hall, New York.
- Paz, M. and Dung, L. (1975), "Power series expansion of the general stiffness matrix for beam elements", Int. J. Numer. Meth. Eng., 9, 449-459. https://doi.org/10.1002/nme.1620090212
- Yesilce, Y. (2010), "Differential transform method for free vibration analysis of a moving beam", Struct. Eng. Mech., 35, 645-658. https://doi.org/10.12989/sem.2010.35.5.645
- Yesilce, Y. (2011), "DTM and DQEM for free vibration of axially loaded and semi-rigid-connected Reddy- Bickford beam", Int. J. Numer. Meth. Bio. Eng., 27, 666-693. https://doi.org/10.1002/cnm.1313
- Yesilce, Y. and Catal, H.H. (2011), "Solution of free vibration equation of semi-rigid connected Reddy-Bickford beams resting on elastic soil using the differential transform method", Arch. Appl. Mech., 81, 199-213. https://doi.org/10.1007/s00419-010-0405-z
- Yesilce, Y. and Catal, S. (2009), "Free vibration of axially loaded Reddy-Bickford beam on elastic soil using differential transform method", Struct. Eng. Mech., 31, 453-475. https://doi.org/10.12989/sem.2009.31.4.453
- Zhou, J.K. (1986), Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China.
Cited by
- Static and dynamic analysis of beam assemblies using a differential system on an oriented graph vol.155, 2015, https://doi.org/10.1016/j.compstruc.2015.02.021
- Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam vol.58, pp.5, 2016, https://doi.org/10.12989/sem.2016.58.5.847
- Differential transform method and numerical assembly technique for free vibration analysis of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and rotary inertias vol.53, pp.3, 2015, https://doi.org/10.12989/sem.2015.53.3.537
- Investigation of bar system modal characteristics using Dynamic Stiffness Matrix polynomial approximations vol.180, 2017, https://doi.org/10.1016/j.compstruc.2016.10.015
- Study on modified differential transform method for free vibration analysis of uniform Euler-Bernoulli beam vol.48, pp.5, 2013, https://doi.org/10.12989/sem.2013.48.5.697
- Dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads vol.44, pp.5, 2012, https://doi.org/10.12989/sem.2012.44.5.681
- Dynamic behavior of axially functionally graded simply supported beams vol.25, pp.6, 2012, https://doi.org/10.12989/sss.2020.25.6.669
- Closed-form solution for mode superposition analysis of continuous beams on flexible supports under moving harmonic loads vol.520, pp.None, 2022, https://doi.org/10.1016/j.jsv.2021.116587