DOI QR코드

DOI QR Code

Dynamic stiffness matrix of an axially loaded slenderdouble-beam element

  • Jun, Li (Vibration, Shock & Noise Institute, Shanghai Jiao Tong University) ;
  • Hongxing, Hua (Vibration, Shock & Noise Institute, Shanghai Jiao Tong University) ;
  • Xiaobin, Li (School of Transportation, Wuhan University of Technology)
  • 투고 : 2006.12.18
  • 심사 : 2010.03.12
  • 발행 : 2010.08.20

초록

The dynamic stiffness matrix is formulated for an axially loaded slender double-beam element in which both beams are homogeneous, prismatic and of the same length by directly solving the governing differential equations of motion of the double-beam element. The Bernoulli-Euler beam theory is used to define the dynamic behaviors of the beams and the effects of the mass of springs and axial force are taken into account in the formulation. The dynamic stiffness method is used for calculation of the exact natural frequencies and mode shapes of the double-beam systems. Numerical results are given for a particular example of axially loaded double-beam system under a variety of boundary conditions, and the exact numerical solutions are shown for the natural frequencies and normal mode shapes. The effects of the axial force and boundary conditions are extensively discussed.

키워드

참고문헌

  1. Aida, T., Toda, S., Ogawa, N. and Imada, Y. (1992), "Vibration control of beams by beam-type dynamic vibration absorbers", J. Eng. Mech., 118, 248-258. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:2(248)
  2. Balkaya, M., Kaya, M.O. and Saglamer, A. (2010), "Free transverse vibrations of an elastically connected simply supported twin pipe system", Struct. Eng. Mech., 34, 549-561. https://doi.org/10.12989/sem.2010.34.5.549
  3. Burden, R.L. and Faires, J.D. (1989), Numerical Analysis, Pws-Kent Publishing Company, Boston.
  4. Char, B.W., Geddes, K.O., Gonnet, G.H., Monagan, M.B. and Watt, S.M. (1990), Maple Reference Manual, Department of Computer Science, University of Waterloo, Symbolic Computation Group and Waterloo Maple Publishing, Canada.
  5. Chen, Y.H. and Sheu, J.T. (1994), "Dynamic characteristics of layered beam with flexible core", J. Vib. Acoust., 116, 350-356. https://doi.org/10.1115/1.2930435
  6. Chonan, S. (1976), "Dynamical behaviours of elastically connected double-beam systems subjected to an impulsive load", T. JSME, 19, 595-603. https://doi.org/10.1299/jsme1958.19.595
  7. De Rosa, M.A. and Lippiello, M. (2007), "Non-classical boundary conditions and DQM for double-beams", Mech. Res. Commun., 34, 538-544. https://doi.org/10.1016/j.mechrescom.2007.08.003
  8. Doyle, J.F. (1997), Wave Propagation in Structures, Springer, New York.
  9. Gopalakrishnan, S., Chakraborty, A. and Mahapatra, D.R. (2008), Spectral Finite Element Method, Springer, London.
  10. Gurgoze, M., Zeren, S. and Bicak, M.M.A. (2008), "On the consideration of the masses of helical springs in damped combined systems consisting of two continua", Struct. Eng. Mech., 28, 167-188. https://doi.org/10.12989/sem.2008.28.2.167
  11. Hamada, T.R., Nakayama, H. and Hayashi, K. (1983), "Free and forced vibrations of elastically connected double-beam systems", T. JSME, 26, 1936-1942. https://doi.org/10.1299/jsme1958.26.1936
  12. 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
  13. Kim, N.I. and Kim, M.Y. (2005), "Exact dynamic element stiffness matrix of shear deformable non-symmetric curved beams subjected to initial axial force", Struct. Eng. Mech., 19, 73-96. https://doi.org/10.12989/sem.2005.19.1.073
  14. Lee, U. (2004), Spectral Element Method in Structural Dynamics, Inha University Press, Incheon.
  15. Leung, A.Y.T. (1993), Dynamic Stiffness and Substructures, Springer, London.
  16. Oniszczuk, Z. (2000), "Free transverse vibrations of elastically connected simply supported double-beam complex system", J. Sound Vib., 232, 387-403. https://doi.org/10.1006/jsvi.1999.2744
  17. 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
  18. Rao, S.S. (1974), "Natural vibrations of systems of elastically connected Timoshenko beams", J. Acoust. Soc. Am., 55, 1232-1237. https://doi.org/10.1121/1.1914690
  19. Ritdumrongkul, S., Abe, M., Fujino, Y. and Miyashita, T. (2004), "Quantitative health monitoring of bolted joints using a piezoceramic actuator-sensor", Smart Mater. Struct., 13, 20-29. https://doi.org/10.1088/0964-1726/13/1/003
  20. Seelig, J.M. and Hoppmann II, W.H. (1964), "Normal mode vibrations of systems of elastically connected parallel bars", J. Acoust. Soc. Am., 36, 93-99. https://doi.org/10.1121/1.1918919
  21. Sisemore, C.L. and Darvennes, C.M. (2002), "Transverse vibration of elastic-viscoelastic-elastic sandwich beams: compression-experimental and analytical study", J. Sound Vib., 252, 155-167. https://doi.org/10.1006/jsvi.2001.4038
  22. Vu, H.V., Ordonez, A.M. and Karnopp, B.H. (2000), "Vibration of a double-beam system", J. Sound Vib., 229, 807-822. https://doi.org/10.1006/jsvi.1999.2528
  23. Zhang, Y.Q., Lu, Y. and Ma, G.W. (2008), "Effect of compressive axial load on forced transverse vibrations of a double-beam system", Int. J. Mech. Sci., 50, 299-305. https://doi.org/10.1016/j.ijmecsci.2007.06.003

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