Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method

Structural Engineering and Mechanics

Volumn 31, Issue 4, 2009, Pages 453-476

  Yesilce, Yusuf ^a   Catal, Seval ^a  

^a Engineering Faculty   (Turkey)

Author keywords

Differential transform method; Elastic soil; Free vibration; Partial differential equation; Reddy Bickford beam

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; FLOW MEASUREMENT; NATURAL FREQUENCIES; PARTIAL DIFFERENTIAL EQUATIONS; SOILS; STIFFNESS; STRUCTURAL PANELS;

AXIAL COMPRESSIVE FORCES; DIFFERENTIAL TRANSFORM METHOD; ELASTIC SOILS; FREE VIBRATION; FREE-VIBRATION ANALYSIS; GOVERNING DIFFERENTIAL EQUATIONS; REDDY-BICKFORD BEAM; TRANSVERSE DISPLACEMENTS;

VIBRATION ANALYSIS;

EID: 61949324487     PISSN: 12254568     EISSN: None     Source Type: Journal    
DOI: 10.12989/sem.2009.31.4.453     Document Type: Article

References (41)

1. Ayaz, F. (2004), "Application of differential transforms method to differential-algebraic equations", Appl. Math. Comput., 152, 648-657.
2. Bert, C.W. and Zeng, H. (2004), "Analysis of axial vibration of compound bars by differential transformation method", J. Sound Vib., 275, 641-647.
3. Bickford, W.B. (1982), "A consistent higher order beam theory", Development Theor. Appl. Mech., 11, 137-150.
4. Bildik, N., Konuralp, A., Bek, F.O. and Küçükarslan, S. (2006), "Solution of different type of the partial differential equation by differential transform method and Adomian's decomposition method", Appl. Math. Comput, 172, 551-567.
5. Çatal, S. (2006), "Analysis of free vibration of beam on elastic soil using differential transform method", Struct. Eng. Mech., 24(1), 51-62.
6. Çatal, S. (2008), "Solution of free vibration equations of beam on elastic soil by using differential transform method", Appl. Math Model., 32, 1744-1757.
7. Çatal, S. and Çatal, H.H. (2006), "Buckling analysis of partially embedded pile in elastic soil using differential transform method", Struct. Eng. Mech., 24(2), 247-268.
8. Chen, C.K. and Ho, S.H. (1996), "Application of differential transformation to eigenvalue problem", J. Appl. Math. Comput, 79, 173-188.
9. 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.
10. Chen, C.L. and Liu, Y.C. (1998), "Solution of two-point boundary-value problems using the differential transformation method", J. Optima. Theory App., 99, 23-35.
11. Cowper, G.R. (1966), "The shear coefficient in Timoshenko's beam theory", J. Appl. Mech., 33(2), 335-340.
12. Doyle, P.F. and Pavlovic, M.N. (1982), "Vibration of beams on partial elastic foundations", J. Earthq. Eng. Struct. Dyn., 10, 663-674.
13. Ertürk, V.S. (2007), "Application of differential transformation method to linear sixth-order boundary value problems", Appl. Math Sci., 1, 51-58.
14. Ertürk, V.S. and Momani, S. (2007), "Comparing numerical methods for solving fourth-order boundary value problems", Appl. Math. Comput., 188, 1963-1968.
15. Esmailzadeh, E. and Ohadi, A.R. (2000), "Vibration and stability analysis of non-uniform Timoshenko beams under axial and distributed tangential loads", J. Sound Vib., 236, 443-456.
16. Gruttmann, F. and Wagner, W. (2001), "Shear coefficient factors in Timoshenko's beam theory for arbitrary shaped cross-section", Comput. Mech., 27, 199-207.
17. Han, S.M., Benaroya, H. and Wei, T. (1999), "Dynamics of transversely vibrating beams using four engineering theories", J. Sound Vib., 225, 935-988.
18. Hassan, I.H.A.H (2002a), "On solving some eigenvalue problems by using differential transformation", Appl. Math. Comput, 121, 1-22.
19. Hassan, I.H.A.H (20026), "Different applications for the differential transformation in the differential equations", Appl. Math. Comput, 129, 183-201.
20. th edn., The University of Michigan Press, Michigan.
21. Heyliger, P.R. and Reddy, J.N. (1988), "A higher-order beam finite element for bending and vibration problems", J. Sound Vib., 126(2), 309-326.
22. Ho, S.H. and Chen, C.K. (2006), "Free transverse vibration of an axially loaded non-uniform sinning twisted Timoshenko beam using differential transform", Int. J. Mech Sci., 48, 1323-1331.
23. 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.
24. Jang, M.J., Chen, C.L. and Liu, Y.C. (2000), "On solving the initial-value problems using differential transformation method", Appl. Math. Comput., 115, 145-160.
25. Kaya, M.O. and Ozgumus, O.O. (2007), "Flexural-torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM", J. Sound Vib., 306, 495-506.
26. Kumaz, A., Oturanç, G and Kiris, M.E. (2005), "n-Dimensional differential transformation method for solving PDEs", Int. J. Comput. Math., 82(3), 369-380.
27. Levinson, M. (1981), "A new rectangular beam theory", J. Sound Vib., 74, 81-87.
28. Malik, M. and Dang, H.H. (1998), "Vibration analysis of continuous systems by differential transformation", Appl. Math Comput, 96, 17-26.
29. Murthy, A.V. (1970), "Vibration of short beams", AIAA, 8, 34-38.
30. Özdemir, Ö. 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.
31. Ozgumus, O.O. and Kaya, M.O. (2006), "Flapwise bending vibration analysis of double tapered rotating Euler-Bernoulli beam by using the differential transform method", Meccanica, 41, 661-670.
32. Ozgumus, O.O. and Kaya, M.O. (2007), "Energy expressions and free vibration analysis of a rotating double tapered Timoshenko beam featuring bending-torsion coupling", Int. J. Eng. Sci., 45, 562-586.
33. Rajasekaran, S. (2008), "Buckling of fully and partially embedded non-prismatic columns using differential quadrature and differential transformation methods", Struct. Eng. Mech., 28(2), 221-238.
34. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, Second Edition, John Wiley, NY
35. Reddy, J.N. (2007), Theory and Analysis of Elastic Plates and Shells, Second Edition, Taylor & Francis; Philadelphia, PA.
36. Timoshenko, S.P. (1921), "On the correction for shear of the differential equation for transverse vibrations of prismatic bars", Philos. Mag., 41, 744-746.
37. Wang, C.M., Reddy, J.N. and Lee, K.H. (2000), Shear Deformable Beams and Plates: Relationships with Classical Solutions, Elsevier Science Ltd., The Netherlands.
38. West, H.H. and Mafi, M. (1984), "Eigenvalues for beam columns on elastic supports", J. Struct. Eng., 110(6), 1305-1320.
39. Yesilce, Y. and Catal, H.H. (2008), "Free vibration of semi-rigid connected Reddy-Bickford piles embedded in elastic soil", Sadhana-Academy Proceedings in Engineering Science, 33(6), 781-801.
40. Yokoyama, T. (1991), "Vibrations of Timoshenko beam-columns on two parameter elastic foundations", Earthq. Eng. Struct. Dyn., 20, 355-370.
41. Zhou, J.K. (1986), Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan China.