Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Free vibration analysis of axially moving beam under non-ideal conditions

  • Bagdatli, Suleyman M. (Faculty of Engineering, Department of Mechanical Engineering, Celal Bayar University) ;
  • Uslu, Bilal (Faculty of Engineering, Department of Mechanical Engineering, Celal Bayar University)
  • Received : 2015.02.25
  • Accepted : 2015.03.30
  • Published : 2015.05.10
⟨ Previous Next ⟩

Abstract

In this study, linear vibrations of an axially moving beam under non-ideal support conditions have been investigated. The main difference of this study from the other studies; the non-ideal clamped support allow minimal rotations and non-ideal simple support carry moment in minimal orders. Axially moving Euler-Bernoulli beam has simple and clamped support conditions that are discussed as combination of ideal and non-ideal boundary with weighting factor (k). Equations of the motion and boundary conditions have been obtained using Hamilton's Principle. Method of Multiple Scales, a perturbation technique, has been employed for solving the linear equations of motion. Linear equations of motion are solved and effects of different parameters on natural frequencies are investigated.

Keywords

References

  1. Bagdatli, S.M., Ozkaya, E. and O z. H.R. (2013), "Dynamics of axially accelerating beams with multiple supports", Nonlin. Dyn., 74, 237-255. https://doi.org/10.1007/s11071-013-0961-1
  2. Bagdatli, S.M., Ozkaya, E. and O z, H.R. (2011), "Dynamics of axially accelerating beams with an intermediate support", J. Vib. Acoust., 33(3), 31013.
  3. Chakraborty, G., Mallik, A.K. and Hatwal, H. (1998), "Non-linear vibration of a travelling beam", Int. J. Nonlin. Mech., 34, 655-670.
  4. Kural, S. and Ozkaya, E. (2012), "Vibrations of an axially accelerating multiple supported flexible beam", Struct. Eng. Mech., 44(4), 521-538. https://doi.org/10.12989/sem.2012.44.4.521
  5. Lee, J. (2013), "Free vibration analysis of beams with non-ideal clamped boundary conditions", J. Mech. Sci. Tech., 27(2), 297-303. https://doi.org/10.1007/s12206-012-1245-2
  6. Nayfeh, A.H. (1981), Introduction to Perturbation Techniques, John Wiley&Sons, USA.
  7. Oz, H.R., Pakdemirli, M. and Boyaci, H. (2001), "Non-linear vibrations and stability of an axially moving beam with time-dependent velocity", Int. J. Nonlin. Mech., 36, 107-115. https://doi.org/10.1016/S0020-7462(99)00090-6
  8. Oz, H.R. (2001), "On the vibrations of an axially travelling beam on fixed supports with variable velocity", J. Sound Vib., 239, 556-564. https://doi.org/10.1006/jsvi.2000.3077
  9. Oz, H.R. and Pakdemirli, M. (1999), "Vibrations of an axially moving beam with time-dependent velocity", J. Sound Vib., 227(2), 239-257. https://doi.org/10.1006/jsvi.1999.2247
  10. Pakdemirli, M. and Boyaci, H. (2002), "Effect of non-ideal boundary conditions on the vibrations of continuous systems", J. Sound Vib., 249, 815-823. https://doi.org/10.1006/jsvi.2001.3760
  11. Pakdemirli, M. and Boyaci, H. (2003), "Non-linear vibrations of a simple-simple beam with a non-ideal support in between", J. Sound Vib., 268(2), 331-241. https://doi.org/10.1016/S0022-460X(03)00363-8
  12. Pakdemirli, M. and Ozkaya, E. (1998), "Approximate boundary layer solution of a moving beam problem", Math. Computat. Appl., 3(2), 93-100.
  13. Pellicano, F. and Zirilli, F. (1998), "Boundary layers and non-linear vibrations in an axially moving beam", Int. J. Nonlin. Mech., 33(4), 691-711. https://doi.org/10.1016/S0020-7462(97)00044-9
  14. Thurman, A.L. and Mote, C.D. (1969), "Free, periodic, nonlinear oscillation of an axially moving strip", J. Appl. Mech., 36, 83. https://doi.org/10.1115/1.3564591
  15. Yurddas, A., Ozkaya, E. and Boyaci, H. (2013), "Nonlinear vibrations of axially moving multi-supported strings having non-ideal support conditions", Nonlin. Dyn., 73, 1223-1244. https://doi.org/10.1007/s11071-012-0650-5
  16. Yurddas, A., O zkaya, E. and Boyaci, H. (2014), "Nonlinear vibrations and stability analysis of axially moving strings having non-ideal mid-support conditions", J. Vib. Control, 20(4), 518-534. https://doi.org/10.1177/1077546312463760

Cited by

  1. Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam vol.55, pp.4, 2015, https://doi.org/10.12989/sem.2015.55.4.871
  2. Forced vibration of axially moving beam with internal resonance in the supercritical regime vol.131-132, 2017, https://doi.org/10.1016/j.ijmecsci.2017.06.038
  3. Closed-form solutions for non-uniform axially loaded Rayleigh cantilever beams vol.60, pp.3, 2016, https://doi.org/10.12989/sem.2016.60.3.455
  4. Dynamic analysis of an axially moving beam subject to inner pressure using finite element method vol.31, pp.6, 2017, https://doi.org/10.1007/s12206-017-0509-2
  5. Non-linear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory vol.80, 2015, https://doi.org/10.1016/j.compositesb.2015.05.030
  6. Irregular instability boundaries of axially accelerating viscoelastic beams with 1:3 internal resonance vol.133, 2017, https://doi.org/10.1016/j.ijmecsci.2017.08.052
  7. Vibrations of fluid conveying microbeams under non-ideal boundary conditions vol.23, pp.10, 2017, https://doi.org/10.1007/s00542-016-3255-y
  8. Non-linear transverse vibrations of tensioned nanobeams using nonlocal beam theory vol.55, pp.2, 2015, https://doi.org/10.12989/sem.2015.55.2.281
  9. Dynamic properties of an axially moving sandwich beam with magnetorheological fluid core vol.9, pp.2, 2017, https://doi.org/10.1177/1687814017693182
  10. Free and forced nonlinear vibration of a transporting belt with pulley support ends vol.92, pp.4, 2018, https://doi.org/10.1007/s11071-018-4179-0
  11. Free vibrations of fluid conveying microbeams under non-ideal boundary conditions vol.24, pp.2, 2015, https://doi.org/10.12989/scs.2017.24.2.141
  12. Free vibration analysis of Euler-Bernoulli beams with non-ideal clamped boundary conditions by using Padé approximation vol.33, pp.3, 2019, https://doi.org/10.1007/s12206-019-0216-2
  13. Nonlinear dynamics of a viscoelastic traveling beam with time-dependent axial velocity and variable axial tension vol.97, pp.1, 2015, https://doi.org/10.1007/s11071-019-04969-9
  14. Bifurcation and chaos of the traveling membrane on oblique supports subjected to external excitation vol.34, pp.11, 2015, https://doi.org/10.1007/s12206-020-1011-9
  15. Nonlinear Phenomena in Axially Moving Beams with Speed-Dependent Tension and Tension-Dependent Speed vol.31, pp.3, 2015, https://doi.org/10.1142/s0218127421500371