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http://dx.doi.org/10.12989/sem.2010.34.5.549

Free transverse vibrations of an elastically connected simply supported twin pipe system  

Balkaya, Muge (Department of Civil Engineering, Istanbul Technical University)
Kaya, Metin O. (Faculty of Aeronautics and Astronautics, Istanbul Technical University)
Saglamer, Ahmet (Department of Civil Engineering, Istanbul Technical University)
Publication Information
Structural Engineering and Mechanics / v.34, no.5, 2010 , pp. 549-561 More about this Journal
Abstract
In this paper, free vibration analyses of a parallel placed twin pipe system simulated by simply supported-simply supported and fixed-fixed Euler-Bernoulli beams resting on Winkler elastic soil are presented. The motion of the system is described by a homogenous set of two partial differential equations, which is solved by a simulation method called the Differential Transform Method (DTM). Free vibrations of an elastically connected twin pipe system are realized by synchronous and asynchronous deflections. The results of the presented theoretical analyses for simply supported Euler-Bernoulli beams are compared with existing ones in open literature and very good agreement is demonstrated.
Keywords
Differential Transform Method; DTM; elastic soil; vibration; twin beam; twin pipeline;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 2  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
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1 Zhou, J.K. (1986), Differential Transformation and its Application for Electrical Circuits, Huazhong University Press, Wuhan, China.
2 Saito, H. and Chonan, S. (1969), "Vibrations of elastically connected double-beam systems", Technology Reports, Tohoku Univ., 34, 141-159.
3 Seelig, J.M. and Hoppmann, W.H. (1964a), "Normal mode vibrations of systems of elastically connected parallel bars", J. Acoust. Soc. Am., 36, 93-99.   DOI
4 Seelig, J.M. and Hoppmann, W.H. (1964b), "Impact on an elastically connected double-beam system", T. Am. Soc. Mech. Eng., J. Appl. Mech., 31, 621-626.   DOI
5 Vu, H.V., Ordonez, A.M. and Karnopp, B.H. (2000), "Vibration of a double-beam system", J. Sound Vib., 229(4), 807-822.   DOI   ScienceOn
6 Winkler, E. (1867), "Die Lehre von der Elastizität und Festigkeit", Prague.
7 Avramidis, I.E. and Morfidis, K. (2006), "Bending of beams on three-parameter elastic foundation", Int. J. Solids Struct., 43, 357-375.   DOI   ScienceOn
8 Ayaz, F. (2003), "On the two-dimensional differential transform method", Appl. Math. Comput., 143, 361-374.   DOI
9 Ayaz, F. (2004), "Solutions of the system of differential equations by differential transform method", Appl. Math. Comput., 147, 547-567.   DOI   ScienceOn
10 Chen, C.K. and Ho, S.H. (1999), "Solving partial differential equations by two-dimensional differential transform method", Appl. Math. Comput., 106, 171-179.   DOI   ScienceOn
11 Catal, S. (2006), "Analysis of free vibration of beam on elastic soil using differential transform method", Struct. Eng. Mech., 24(1), 51-62.   DOI
12 Erol, H. and Gurgoze, M. (2004), "Longitudinal vibrations of a double-rod system coupled by springs and dampers", J. Sound Vib., 276, 419-430.   DOI
13 Abu-Hilal, M. (2006), "Dynamic response of a double Euler-Bernoulli beam due to a moving constant load", J. Sound Vib., 297, 477-491.   DOI
14 Arikoglu, A. and Ozkol, I. (2005), "Solution of boundary value problems for integro-differential equations by using differential transform method", Appl. Math. Comput., 168, 1145-1158.   DOI   ScienceOn
15 Ozdemir, O. and Kaya, M.O. (2006b), "Flapwise bending vibration analysis of double tapered rotating Euler- Bernoulli beam by using the differential transform method", Meccanica, 41(6), 661-670.   DOI   ScienceOn
16 Oniszczuk, Z. (2002), "Free transverse vibrations of an elastically connected complex beam-string system", J. Sound Vib., 254, 703-715.   DOI   ScienceOn
17 Oniszczuk, Z. (2003), "Forced transverse vibrations of an elastically connected complex simply supported double-beam system", J. Sound Vib., 264, 273-286.   DOI   ScienceOn
18 Ozdemir, O. and Kaya, M.O. (2006a), "Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli-Euler beam by differential transform method", J. Sound Vib., 289, 413-420.   DOI   ScienceOn
19 Kukla, S. and Skalmierski, B. (1994), "Free vibration of a system composed of two beams separated by an elastic layer", J. Theor. Appl. Mech., 32, 581-590.
20 Oniszczuk, Z. (1999), "Transverse vibrations of elastically connected rectangular double-membrane compound system", J. Sound Vib., 221, 235-250.   DOI   ScienceOn
21 Oniszczuk, Z. (2000a), "Free transverse vibrations of elastically connected simply supported double-beam complex system", J. Sound Vib., 232(2), 387-403.   DOI   ScienceOn
22 Oniszczuk, Z. (2000b), "Forced transverse vibrations of an elastically connected double-beam complex system", XVII Ogolnopolska Konferencza Naukowo-Dydaktyczna Teorii Maszyn 1 Mechanizmow, Warszawa- Jachranka, 6-8, Wrzesnia.
23 Hamada, T.R., Nakayama, H. and Hayashi, K. (1983), "Free and forced vibrations of elastically connected double-beam systems", Trans. Japan Soc.Mech. Eng., 49, 289-295.   DOI
24 Kukla, S. (1994), "Free vibration of the system of two beams connected by many translational springs", J. Sound Vib., 172, 130-135.   DOI   ScienceOn
25 Kaya, M.O. (2006), "Free vibration analysis of rotating Timoshenko beam by differential transform method", Aircr. Eng. Aerosp. Tec., 78(3), 194-203.   DOI   ScienceOn
26 Kessel, P.G. (1966), "Resonances excited in an elastically connected double-beam system by a cyclic moving load", J. Acoust. Soc. Am. 40, 684-687.   DOI
27 Kessel, P.G. and Raske, T.F. (1971), "Damped response of an elastically connected double-beam system due to a cyclic moving load", J. Acoust. Soc. Am., 49, 371-373.   DOI