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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)
  • 투고 : 2007.01.11
  • 심사 : 2007.08.08
  • 발행 : 2010.03.30

초록

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.

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참고문헌

  1. Abu-Hilal, M. (2006), "Dynamic response of a double Euler-Bernoulli beam due to a moving constant load", J. Sound Vib., 297, 477-491. https://doi.org/10.1016/j.jsv.2006.03.050
  2. 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. https://doi.org/10.1016/j.amc.2004.10.009
  3. Avramidis, I.E. and Morfidis, K. (2006), "Bending of beams on three-parameter elastic foundation", Int. J. Solids Struct., 43, 357-375. https://doi.org/10.1016/j.ijsolstr.2005.03.033
  4. Ayaz, F. (2003), "On the two-dimensional differential transform method", Appl. Math. Comput., 143, 361-374. https://doi.org/10.1016/S0096-3003(02)00368-5
  5. Ayaz, F. (2004), "Solutions of the system of differential equations by differential transform method", Appl. Math. Comput., 147, 547-567. https://doi.org/10.1016/S0096-3003(02)00794-4
  6. Chen, C.K. and Ho, S.H. (1999), "Solving partial differential equations by two-dimensional differential transform method", Appl. Math. Comput., 106, 171-179. https://doi.org/10.1016/S0096-3003(98)10115-7
  7. Catal, S. (2006), "Analysis of free vibration of beam on elastic soil using differential transform method", Struct. Eng. Mech., 24(1), 51-62. https://doi.org/10.12989/sem.2006.24.1.051
  8. Erol, H. and Gurgoze, M. (2004), "Longitudinal vibrations of a double-rod system coupled by springs and dampers", J. Sound Vib., 276, 419-430. https://doi.org/10.1016/j.jsv.2003.10.043
  9. 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. https://doi.org/10.1299/kikaic.49.289
  10. Kaya, M.O. (2006), "Free vibration analysis of rotating Timoshenko beam by differential transform method", Aircr. Eng. Aerosp. Tec., 78(3), 194-203. https://doi.org/10.1108/17488840610663657
  11. 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. https://doi.org/10.1121/1.1910136
  12. 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. https://doi.org/10.1121/1.1912341
  13. Kukla, S. (1994), "Free vibration of the system of two beams connected by many translational springs", J. Sound Vib., 172, 130-135. https://doi.org/10.1006/jsvi.1994.1163
  14. 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.
  15. Oniszczuk, Z. (1999), "Transverse vibrations of elastically connected rectangular double-membrane compound system", J. Sound Vib., 221, 235-250. https://doi.org/10.1006/jsvi.1998.1998
  16. Oniszczuk, Z. (2000a), "Free transverse vibrations of elastically connected simply supported double-beam complex system", J. Sound Vib., 232(2), 387-403. https://doi.org/10.1006/jsvi.1999.2744
  17. 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.
  18. Oniszczuk, Z. (2002), "Free transverse vibrations of an elastically connected complex beam-string system", J. Sound Vib., 254, 703-715. https://doi.org/10.1006/jsvi.2001.4117
  19. Oniszczuk, Z. (2003), "Forced transverse vibrations of an elastically connected complex simply supported double-beam system", J. Sound Vib., 264, 273-286. https://doi.org/10.1016/S0022-460X(02)01166-5
  20. 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. https://doi.org/10.1016/j.jsv.2005.01.055
  21. 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. https://doi.org/10.1007/s11012-006-9012-z
  22. Saito, H. and Chonan, S. (1969), "Vibrations of elastically connected double-beam systems", Technology Reports, Tohoku Univ., 34, 141-159.
  23. 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. https://doi.org/10.1121/1.1918919
  24. 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. https://doi.org/10.1115/1.3629723
  25. Vu, H.V., Ordonez, A.M. and Karnopp, B.H. (2000), "Vibration of a double-beam system", J. Sound Vib., 229(4), 807-822. https://doi.org/10.1006/jsvi.1999.2528
  26. Winkler, E. (1867), "Die Lehre von der Elastizität und Festigkeit", Prague.
  27. Zhou, J.K. (1986), Differential Transformation and its Application for Electrical Circuits, Huazhong University Press, Wuhan, China.

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