Advertisement

Archive of Applied Mechanics

, Volume 88, Issue 7, pp 1041–1057 | Cite as

Vibration and buckling of a multiple-Timoshenko beam system joined by intermediate elastic connections under compressive axial loading

  • S. Foroozandeh
  • A. Ariaei
Original
  • 156 Downloads

Abstract

Free vibration and buckling of a set of parallel Timoshenko beams joined by intermediate flexible connections under axial loading are assessed in this paper. The numbers of beams and intermediate connections are arbitrary. Through axial loading, a new set of equations is extracted, applicable in solving the axial loading problems. The existence of the intermediate connections and the related compatibility equations allow for the introduction of coupled partial differential equations. The solution involves a change of variables to uncouple the governing differential equations. The natural frequencies and mode shapes are calculated through the transfer matrix method. By presenting an appropriate equation, it is observed that the general formulation studied here, regarding the separated flexible connections, can easily cover the issue of parallel beams joined by Winkler elastic layers in a continuous manner presented in the literature. The effects of different parameters such as the number of beams, number and stiffness of elastic connections and axial loading are assessed on the natural frequencies and the critical buckling force.

Keywords

Multiple-Timoshenko beam system Intermediate flexible connections Axial loading Critical buckling force Winkler elastic layer 

References

  1. 1.
    Stojanović, V., Kozić, P., Pavlović, R., Janevski, G.: Effect of rotary inertia and shear on vibration and buckling of a double beam system under compressive axial loading. Arch. Appl. Mech. 81, 1993–2005 (2011)CrossRefzbMATHGoogle Scholar
  2. 2.
    Şimşek, M., Cansız, S.: Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load. Compos. Struct. 94, 2861–2878 (2012)CrossRefGoogle Scholar
  3. 3.
    Kukla, S.: Free vibration of the system of two beams connected by many translational springs. J. Sound Vib. 172, 130–135 (1994)CrossRefzbMATHGoogle Scholar
  4. 4.
    Oniszczuk, Z.: Free transverse vibrations of elastically connected simply supported double-beam complex system. J. Sound Vib. 232, 387–403 (2000)CrossRefGoogle Scholar
  5. 5.
    Oniszczuk, Z.: Forced transverse vibrations of an elastically connected complex simply supported double-beam system. J. Sound Vib. 264, 273–286 (2003)CrossRefzbMATHGoogle Scholar
  6. 6.
    Li, Y.X., Sun, L.Z.: Transverse vibration of an undamped elastically connected double-beam system with arbitrary boundary conditions. J. Eng. Mech. 142(2), 04015070 (2016)CrossRefGoogle Scholar
  7. 7.
    Zhang, Y.Q., Lu, Y., Wang, S.L., Liu, X.: Vibration and buckling of a double-beam system under compressive axial loading. J. Sound Vib. 318, 341–352 (2008)CrossRefGoogle Scholar
  8. 8.
    Zhang, Y.Q., Lu, Y., Ma, G.W.: Effect of compressive axial load on forced transverse vibrations of a double-beam system. Int. J. Mech. Sci. 50, 299–305 (2008)CrossRefzbMATHGoogle Scholar
  9. 9.
    Vu, H.V., Ordonez, A.M., Karnopp, B.H.: Vibration of a double-beam system. J. Sound Vib. 229, 807–822 (2000)CrossRefzbMATHGoogle Scholar
  10. 10.
    Abu-Hilal, M.: Dynamic response of a double Euler–Bernoulli beam due to a moving constant load. J. Sound Vib. 297, 477–491 (2006)CrossRefGoogle Scholar
  11. 11.
    Stojanović, V., Kozić, P.: Forced transverse vibration of Rayleigh and Timoshenko double-beam system with effect of compressive axial load. Int. J. Mech. Sci. 60, 59–71 (2012)CrossRefGoogle Scholar
  12. 12.
    Mirzabeigy, A., Madoliat, R., Vahabi, M.: Free vibration analysis of two parallel beams connected together through variable stiffness elastic layer with elastically restrained ends. Adv. Struct. Eng. 20, 275–287 (2017)CrossRefGoogle Scholar
  13. 13.
    Rezaiee-Pajand, M., Hozhabrossadati, S.M.: Analytical and numerical method for free vibration of double-axially functionally graded beams. Compos. Struct. 152, 488–498 (2016)CrossRefGoogle Scholar
  14. 14.
    Stojanović, V., Kozić, P., Janevski, G.: Exact closed-form solutions for the natural frequencies and stability of elastically connected multiple beam system using Timoshenko and high-order shear deformation theory. J. Sound Vib. 332, 563–576 (2013)CrossRefGoogle Scholar
  15. 15.
    Stojanović, V., Kozić, P.: Vibrations and Stability of Complex Beam Systems. Springer International Publishing, Berlin (2015)CrossRefzbMATHGoogle Scholar
  16. 16.
    Ariaei, A., Ziaei-Rad, S., Ghayour, M.: Transverse vibration of a multiple-Timoshenko beam system with intermediate elastic connections due to a moving load. Arch. Appl. Mech. 81, 263–281 (2010)CrossRefzbMATHGoogle Scholar
  17. 17.
    Li, J., Chen, Y., Hua, H.: Exact dynamic stiffness matrix of a Timoshenko-three-beam system. Int. J. Mech. Sci. 50, 1023–1034 (2008)CrossRefzbMATHGoogle Scholar
  18. 18.
    Ghafarian, M., Ariaei, A.: Free vibration analysis of a system of elastically interconnected rotating tapered Timoshenko beams using differential transform method. Int. J. Mech. Sci. 107, 93–109 (2016)CrossRefGoogle Scholar
  19. 19.
    Kelly, S.G., Srinivas, S.: Free vibrations of elastically connected stretched beams. J. Sound Vib. 326, 883–893 (2009)CrossRefGoogle Scholar
  20. 20.
    Ariaei, A., Ziaei-Rad, S., Malekzadeh, M.: Dynamic response of a multi-span Timoshenko beam with internal and external flexible constraints subject to a moving mass. Arch. Appl. Mech. 83, 1257–1272 (2013)CrossRefzbMATHGoogle Scholar
  21. 21.
    Civalek, Ö., Kiracioglu, O.: Free vibration analysis of Timoshenko beams by DSC method. Int. J. Numer. Methods Biomed. Eng. 26, 1890–1898 (2010)zbMATHGoogle Scholar
  22. 22.
    Ghayesh, M.H., Kazemirad, S., Darabi, M.A., Woo, P.: Thermo-mechanical nonlinear vibration analysis of a spring-mass-beam system. Arch. Appl. Mech. 82, 317–331 (2012)CrossRefzbMATHGoogle Scholar
  23. 23.
    Zhu, T.L.: Free flapewise vibration analysis of rotating double-tapered Timoshenko beams. Arch. Appl. Mech. 82, 479–494 (2012)CrossRefzbMATHGoogle Scholar
  24. 24.
    Timoshenko, P.S., Gere, M.J.: Theory of Elastic Stability, 2nd edn. McGraw-Hill, New York (1964)Google Scholar
  25. 25.
    Caddem, S., Caliò, I.: The influence of the axial force on the vibration of the Euler-Bernoulli beam with an arbitrary number of cracks. Arch. Appl. Mech. 82, 827–839 (2012)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of EngineeringUniversity of IsfahanIsfahanIran

Personalised recommendations