DOI QR코드

DOI QR Code

Non linear vibrations of stepped beam systems using artificial neural networks

  • Bagdatli, S.M. (Department of Mechanical Engineering, Celal Bayar University) ;
  • Ozkaya, E. (Department of Mechanical Engineering, Celal Bayar University) ;
  • Ozyigit, H.A. (Department of Mechanical Engineering, Zonguldak Karaelmas University) ;
  • Tekin, A. (Celal Bayar University)
  • 투고 : 2008.02.05
  • 심사 : 2009.07.02
  • 발행 : 2009.09.10

초록

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained by using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Natural frequencies are calculated for different boundary conditions, stepped ratios and stepped locations by Newton-Raphson Method. The corresponding nonlinear correction coefficients are also calculated for the fundamental mode. At the second part, an alternative method is produced for the analysis. The calculated natural frequencies and nonlinear corrections are used for training an artificial neural network (ANN) program which has a multi-layer, feed-forward, back-propagation algorithm. The results of the algorithm produce errors less than 2.5% for linear case and 10.12% for nonlinear case. The errors are much lower for most cases except clamped-clamped end condition. By employing the ANN algorithm, the natural frequencies and nonlinear corrections are easily calculated by little errors, and the computational time is drastically reduced compared with the conventional numerical techniques.

키워드

과제정보

연구 과제 주관 기관 : Technical Research Council of Turkey (TUBITAK)

참고문헌

  1. Aldraihem, O.J. and Baz, A. (2002), "Dynamic stability of stepped beams under moving loads", J. Sound Vib., 250(5), 835-848. https://doi.org/10.1006/jsvi.2001.3976
  2. Aydogdu, M. and Taskin, V. (2007), "Free vibration analysis of functionally graded beams with simply supported edges", Mater. Des., 28(5), 1651-1656. https://doi.org/10.1016/j.matdes.2006.02.007
  3. Balasubramanian, T.S., Subramanian, G. and Ramani, T.S. (1990), "Significance and use of very high order derivatives as nodal degrees of freedom in stepped beam vibration analysis", J. Sound Vib., 137, 353-356. https://doi.org/10.1016/0022-460X(90)90803-8
  4. Durmu , H.K., Ozkaya, E. and Meric, C. (2006), "The use of neural networks for the prediction of wear loss and surface roughness of AA 6351 aluminum alloy", Mater. Des., 27, 156-159. https://doi.org/10.1016/j.matdes.2004.09.011
  5. Hou, J.W. and Yuan, J.Z. (1998), "Calculation of eigenvalue and eigenvector derivatives for nonlinear beam vibrations", Am. Inst. Aeronaut. Astronaut. J., 26, 872-880.
  6. Jang, S.K. and Bert, C.W. (1989), "Free Vibration of stepped beams: Exact and numerical solutions", J. Sound Vib., 130(2), 342-346. https://doi.org/10.1016/0022-460X(89)90561-0
  7. Jang, S.K. and Bert, C.W. (1989), "Free vibrations of stepped beams: higher mode frequencies and effects of steps on frequency", J. Sound Vib., 132, 164-168. https://doi.org/10.1016/0022-460X(89)90882-1
  8. Karl k, B., Ozkaya E., Ayd n, S. and Pakdemirli M. (1998), "Vibrations of beam-mass systems using artificial neural networks", Comput. Struct., 69, 339-347. https://doi.org/10.1016/S0045-7949(98)00126-6
  9. Krishnan, A., George, G. and Malathi, P. (1998), "Use of finite difference method in the study of stepped beams", Int. J. Mech. Eng. Edu., 26, 11-24. https://doi.org/10.1177/030641909802600103
  10. Kwon, H.D. and Park, Y.P. (2002), "Dynamic characteristics of stepped cantilever beams connected with a rigid body", J. Sound Vib., 255(4), 701-717. https://doi.org/10.1006/jsvi.2001.4185
  11. McDonald, P.H. (1991), "Nonlinear dynamics of a beam", Comput. Struct., 40, 1315-1320. https://doi.org/10.1016/0045-7949(91)90401-7
  12. Naguleswaran, S. (2002), "Natural frequencies, sensitivity and mode shape details of an Euler-Bernoulli beam with one-step change in cross-section and with ends on classical supports", J. Sound Vib., 252, 751-767. https://doi.org/10.1006/jsvi.2001.3743
  13. Naguleswaran, S. (2003), "Vibration and stability of an Euler-Bernoulli beam with up to three step changes in cross section and axial force", Int. J. Mech. Sci., 45, 1563-1579. https://doi.org/10.1016/j.ijmecsci.2003.09.001
  14. Pakdemirli, M. and Nayfeh, A. (1994), "Nonlinear vibration of a beam-spring-mass system", J. Vib. Acoust., 166, 433-438.
  15. Qaisi, M.I. (1997), "A power series solution for the nonlinear vibrations of beams", J. Sound Vib., 199, 587-594. https://doi.org/10.1006/jsvi.1996.0696
  16. Cetinel, H., Ozyi it, H.A. and Özsoyeller, L. (2002), "Artificial neural networks modelling of mechanical property and microstructure evolution in the tempcore process", Comput. Struct., 80, 213-218. https://doi.org/10.1016/S0045-7949(02)00016-0
  17. Cevik, M., Ozkaya, E. and Pakdemirli, M. (2002), "Natural frequencies of suspension bridges: An artificial neural network approach", J. Sound Vib., 257(3), 596-604. https://doi.org/10.1006/jsvi.2001.4237
  18. Oz, H.R., Pakdemirli, M., Ozkaya, E. and Y lmaz, M. (1998), "Non-linear vibrations of a slight curved beam resting on a non-linear elastic foundation", J. Sound Vib., 221(3), 295-309.
  19. Ozkaya, E. (2002), "Non-linear transverse vibrations of a simply supported beam carrying concentrated masses", J. Sound Vib., 257, 413-424. https://doi.org/10.1006/jsvi.2002.5042
  20. Ozkaya, E. and Pakdemirli, M. (1999), "Nonlinear vibrations of a beam-mass system with both ends clamped", J. Sound Vib., 221(3), 491-503. https://doi.org/10.1006/jsvi.1998.2003
  21. Ozkaya, E. and Tekin, A. (2007), "Non-linear vibrations of stepped beam system under different boundary conditions", Struct. Eng. Mech., 27(3), 333-345. https://doi.org/10.12989/sem.2007.27.3.333
  22. Ozkaya, E. and Oz, H.R. (2002), "Determinations of natural frequencies and stability regions of axially moving beams using artificial neural networks method", J. Sound Vib., 252(4), 782-789. https://doi.org/10.1006/jsvi.2001.3991
  23. Ozkaya, E., Pakdemirli, M. and Oz, H.R. (1997), "Nonlinear vibrations of a beam-mass system under different boundary conditions", J. Sound Vib., 199, 679-696. https://doi.org/10.1006/jsvi.1996.0663

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