Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Construction of the shape functions of beam vibrations for analysis of the rectangular plates by Kantorovich-Vlasov's method

  • Olodo, Emmanuel E.T. (Laboratory of Applied Mechanics and Energetic (LEMA), University of Abomey-Calavi) ;
  • Degan, Gerard (Laboratory of Applied Mechanics and Energetic (LEMA), University of Abomey-Calavi)
  • Received : 2013.12.15
  • Accepted : 2014.07.25
  • Published : 2014.11.10
⟨ Previous Next ⟩

Abstract

For analysis of the plates and membranes by numerical or analytical methods, the question of choice of the system of functions satisfying the different boundary conditions remains a major challenge to address. It is to this issue that is dedicated this work based on an approach of choice of combinations of trigonometric functions, which are shape functions of a bended beam with the boundary conditions corresponding to the plate support mode. To do this, the shape functions of beam vibrations for strength analysis of the rectangular plates by Kantorovich-Vlasov's method is considered. Using the properties of quasi-orthogonality of those functions allowed assessing to differential equation for every member of the series. Therefore it's proposed some new forms of integration of the beam functions, in order to simplify the problem.

Keywords

References

  1. Azzar, L., Benamar, R. and White, R.G. (2002), "A semi-analytical approach to the non-linear dynamic response of beams at large amplitudes", J. Sound Vib., 224(2),183-207.
  2. Bors, I., Milchis, T. and Popescu, M. (2013), "Nonlinear vibration of elastic beams", Acta Tech. Nap., Civil Eng. Arch., 56(1), 51-56.
  3. Caddemi, S., Calio, I. and Rapicavoli, D. (2013), "A novel beamfinite element with singularities for the dynamic analysis of discontinuous frames", Arch. Appl. Mech., 83(10), 1451-1468. https://doi.org/10.1007/s00419-013-0757-2
  4. Curnier, A. (2005), Mecanique Des Solides Deformables 1 : Cinematique, Dynamique, Energetique PPUB, Lausanne, Suisse.
  5. Daya, E.M., Azzar, L. and Potier-Ferry, M. (2004), "An amplitude equation for the non-linear vibration of viscoelastically damped sandwich beam", J. Sound Vib., 271(3-5) ,789-813. https://doi.org/10.1016/S0022-460X(03)00754-5
  6. Ekwaro-Osire, S., Maithripala, D.H.S. and Berg, J.M. (2001), "A series expansion approach to interpreting the spctra of the Timoshenko beam", J. Sound Vib., 204(4), 667-678.
  7. Ezeh, J.C., Ibearugbulem, O.M., Njoku, K.O. and Ettu, L.O. (2013), "Dynamic analysis of isotropic SSSS plate using taylor series shape function in Galerkin's functional", Int. J. Em. Tech. Adv. Eng., 3(5), 372-375.
  8. Han, S.M., Benaroya, H. and Wei, T. (1999), "Dynamics of transversely vibrating beams using four engineering theories", J. Sound Vib., 225(5), 935-988. https://doi.org/10.1006/jsvi.1999.2257
  9. Iakimov, S.K. (1971), Raschet balok na uprugom osnovanii, Leningrad.
  10. Jelenic, G. and Papa, E. (20011), "Exact solution for 3D Timoshenko beam problem using linked interpolation of arbitrary order", Arch. Appl. Mech., 81(2), 171-183.
  11. Kazakov, K.S. (2012), "Elastodynamic infinite elements based on modified Bessel shape functions, applicable in the finte element method", Struct. Eng. Mech., 42(3), 353-362. https://doi.org/10.12989/sem.2012.42.3.353
  12. Krylov, A.N. (1931), O raschete balok lezhashchikh na uprugom osnovanii, Akademiia nauk SSSR, Moskva, Russia,
  13. Misra, R.K. (2012), "Free vibration analysis of isotropic plate, using multiquadric radial basis function", Int. J. Sci. Environ. Tech., 2, 99-107.
  14. Ning, L., Zhongxian, L. and Lili, X. (2013), "A fiber-section bsed Timoshenko beam element using shearbending interdependent shape function", Earthq. Eng. Eng. Vib., 12, 421-432. https://doi.org/10.1007/s11803-013-0183-z
  15. Rakotomanana, L. (2004), A Geometric Approach To Thermomechanics Of Dissipating Continua, Progress in Mathematical Physics , Birkhauser, Boston, USA.
  16. Timoshenko, S.P. (1985), Vibration In Engineering, Science, Moscow, Russia.
  17. Triantafyllou, S. and Koumousis, V. (2011), "An inelastic Timoshenko beam element with axial-shearflexural interaction", Comput. Mech., 48(6) ,713-727. https://doi.org/10.1007/s00466-011-0616-3
  18. Xi, L.Y., Li, X.F. and Tang, G.J. (2013), "Free vibration of standing and handing gravity-loaded Rayleigh cantilevers", Int. J. Mech. Sci., 66,233-238. https://doi.org/10.1016/j.ijmecsci.2012.11.013
  19. Yufeng, X. and Liu, B. (2009), "New exact solutions for free vibrations of rectangular thin plates by sympletic dual method", Act Mech. Sin., 25, 265-270. https://doi.org/10.1007/s10409-008-0208-4