References
- Aydogan, M. (1995), 'Stiffness-matrix formulation of beams with shear effect on elastic foundation', J. Struct. Eng., ASCE, 121, 1265-1270 https://doi.org/10.1061/(ASCE)0733-9445(1995)121:9(1265)
- Banarje, J.R. and Williams, F.W. (1994), 'The effect of shear deformation on the critical buckling of columns', J. Sound Vib., 174, 607-616 https://doi.org/10.1006/jsvi.1994.1297
- Budkowska, B.B. and Sozymczak, C. (1996), 'Initial post-buckling behavior of piles partially embedded in soil', Comput. Struct., 62, 831-835 https://doi.org/10.1016/S0045-7949(96)00302-1
- Capron, M.D. and Williams, F.W. (1988), 'Exact dynamic stiffness for an axially loaded uniform Timoshenko member embedded in an elastic medium', J. Sound Vib., 124, 453-466 https://doi.org/10.1016/S0022-460X(88)81387-7
- Catal, H.H. (2002), 'Free vibration of partially supported piles with the effects of bending moment, axial and shear force', Eng. Struct., 24, 1615-1622 https://doi.org/10.1016/S0141-0296(02)00113-X
- Catal, H.H. and Alku, S. (1996a), 'Calculation of the second order stiffness matrix of the beam on elastic foundation', Turkish J. Eng. Envir. Sci. TUBITAK. 20, 145-201
- Catal, H.H. and Alku, S. (1996b), 'Comparison solutions of the continuous footing subjected to bending moment, shear and axial force using finite difference equations and matrix-displacement methods', Proc. of 2nd. National Computational Mechanic Congress, 121-129, Trabzon, Turkey, September
- Chen, C.K. and Ho, S.H. (1996), 'Application of differential transformation to eigenvalue problem', J. Appl. Math. Comput., 79, 173-178 https://doi.org/10.1016/0096-3003(95)00253-7
- Chen, C.N. (1998), 'Solution of beam on elastic foundation by DQEM', J. Eng. Mech., 124, 1381-1384 https://doi.org/10.1061/(ASCE)0733-9399(1998)124:12(1381)
- Chen, Y. (1997), 'Assessment on pile effective lengths and their effects on design I and II', Comput. Struct., 62, 265-286 https://doi.org/10.1016/S0045-7949(96)00201-5
- Doyle, P. and Pavlovic, M. (1982), 'Vibrations of beam on partial elastic foundations', Earthq. Eng. Struct. Dyn., 10, 663-674 https://doi.org/10.1002/eqe.4290100504
- Erguven, M.E. and Gedikli, A. (2003), 'A mixed finite element formulation for Timoshenko beam on Winkler foundation', Comput. Mech., 31, 229-237
- Heelis, M.E., Pavlovic, M.N. and West, R.P. (1999), 'The stability of uniform-friction piles in homogeneous and non-homogeneous elastic foundations', Int. J. Solids Struct., 36, 3277-3292 https://doi.org/10.1016/S0020-7683(98)00150-4
- Heelis, M.E., Pavlovic, M.N. and West, R.P. (2004), 'The analytical prediction of the buckling loads of fully and partially embedded piles', Geotechnique, 54, 363-373 https://doi.org/10.1680/geot.2004.54.6.363
- Hetenyi, M. (1995), Beams on Elastic Foundations. The University of Michigan Press, Michigan
- Hosking, R.J., Husain, S.A. and Milinazzo, F. (2004), 'Natural flexural vibrations of a continuous beam on discrete elastic supports', J. Sound Vib., 272, 169-185 https://doi.org/10.1016/S0022-460X(03)00325-0
- Hsieh, S.C., Chen, J.H. and Lee, A.C. (2006), 'A modified transfer matrix method for coupling lateral and torsional vibrations of symmetric rotor bearing systems', J. Sound Vib., 209, 294-333
- Jang, M.J. and Chen, C.L. (1997), 'Analysis of response of 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
- Li, Q.S. (2001a), 'Buckling of multi-step cracked columns with shear deformation', Eng. Struct., 23, 356-364 https://doi.org/10.1016/S0141-0296(00)00047-X
- Li, Q.S. (2001b), 'Buckling of multi-step non-uniform beams with elastically restrained boundary conditions', J. Construct. Steel Res., 57, 753-777 https://doi.org/10.1016/S0143-974X(01)00010-4
- Malik, M. and Dang, H.H. (1998), 'Vibration analysis of continuous systems by differential transformation', Appl. Math. Comput., 97, 17-26 https://doi.org/10.1016/S0096-3003(97)10153-9
- Ozdemir, O. and Kaya, M.O. (2006), 'Flapwise bending vibration analysis of a 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
- Pavlovic, M.N. and Tsikkos, S. (1982), 'Beams on quasi-Winkler foundations', Eng. Struct., 4, 113-118 https://doi.org/10.1016/0141-0296(82)90045-1
- Reddy, A.S. and Vasangkar, A.J. (1970), 'Buckling of fully and partially embedded piles', J. Soil Mech. Foundations Div., 96, 1951-1965
- Ross, S.L. (1984), Differential Equations. Third Edition, John Wiley & Sons, New York
- Ruotolu, R. and Surace, C. (2004), 'Natural frequencies of a bar with multiple cracks', J. Sound Vib., 272, 301-316 https://doi.org/10.1016/S0022-460X(03)00761-2
- Smith, I.M. (1979), 'Discrete element analysis of pile instability', Int. J. Numer. Analytical Methods in Geomechanics, 3, 205-211 https://doi.org/10.1002/nag.1610030208
- Valsangkar, A.J. and Pradhanang, R.B. (1987), 'Vibration of partially supported piles', J. Eng. Mech., 113, 1244-1247 https://doi.org/10.1061/(ASCE)0733-9399(1987)113:8(1244)
- Wang, C.M., Ng, K.H. and Kitipornchai, S. (2002), 'Stability criteria for Timoshenko columns with intermediate and end concentrated axial loads', J. Construct. Steel Res., 58, 1177-1193 https://doi.org/10.1016/S0143-974X(01)00071-2
- West, H.H. and Mati, M. (1984), 'Eigenvalues for beam-columns on elastic supports', J. Struct. Eng., ASCE, 110, 1305-1319 https://doi.org/10.1061/(ASCE)0733-9445(1984)110:6(1305)
- West, R.P., Heelis, M.E., Pavlovic, M.N. and Wylie, G.B. (1997), 'Stability of end-bearing piles in a non-homogeneous elastic foundation', Int. J. Numer. Analytical Methods in Geomechanics, 21, 845-861 https://doi.org/10.1002/(SICI)1096-9853(199712)21:12<845::AID-NAG905>3.0.CO;2-7
- Yang, J. and Ye, J.Q. (2002), 'Dynamic elastic local buckling of piles under impact loads', Struct. Eng. Mech., 13, 543-556 https://doi.org/10.12989/sem.2002.13.5.543
- Zhou, J.K. (1986), Differential Transformation and Its Applications for Electrical Circuits, Wuhan China, Huazhong University Press
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