Advertisement

Vibration of an SDOF Representing a Rigid Beam Supported by Two Unequal Columns with One Mounted on a Flexible Base

  • Lila Chalah-Rezgui
  • Farid Chalah
  • Salah Eddine Djellab
  • Ammar Nechnech
  • Abderrahim Bali
Chapter
  • 60 Downloads
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 124)

Abstract

The structural dynamic analysis considers a basic mechanical vibrating system to represent a single degree of freedom. Such a system commonly formed by an infinitely rigid beam supported by two columns is used to establish the dynamic equilibrium equation. The analyzed single degree of freedom noted 1-DOF in this contribution considers different heights for the columns while a torsion spring is disposed at the first column base. Thus, the lateral stiffness is constituted by the sum of the contributions of the first column, the torsional spring, and the second column. This study allowed the determination of the vibration period of the 1-DOF by using the finite element method for various heights ratios and different values of the torsion spring stiffness. The findings of the conducted investigations are presented on plotted curves giving the vibration period T as a function of both the heights ratio and the torsion spring stiffness value.

Keywords

Frame One story Torsion spring Column stiffness Unequal heights 

References

  1. 1.
    Bathe, K.-J.: Finite Element Procedures. Prentice-Hall, Englewood Cliffs, NJ (2014)zbMATHGoogle Scholar
  2. 2.
    Bathe, K.-J., Wilson, E.L.: Solution methods for eigenvalue problems in structural mechanics. Int. J. Numer. Meth. Eng. 6, 213–226 (1973).  https://doi.org/10.1002/nme.1620060207CrossRefzbMATHGoogle Scholar
  3. 3.
    Clough, R.W., Penzien, J.: Dynamics of Structures. McGraw-Hill, New York (1975)zbMATHGoogle Scholar
  4. 4.
    Liu, W.H., Wu, J.-R., Huang, C.-C.: Free vibration of beams with elastically restrained edges and intermediate concentrated masses. J. Sound Vib. 122, 193–207 (1988).  https://doi.org/10.1016/S0022-460X(88)80348-1CrossRefGoogle Scholar
  5. 5.
    Maurizi, M.J., Rossi, R.E., Reyes, J.A.: Vibration frequencies for a uniform beam with one end spring-hinged and subjected to a translational restraint at the other end. J. Sound Vib. 48, 565–568 (1976).  https://doi.org/10.1016/0022-460X(76)90559-9CrossRefGoogle Scholar
  6. 6.
    Paz, M.: Structural Dynamics, Theory and Computation. Van Nostrand Reinhold Environmental Engineering Series. Van Nostrand Reinhold, New York (1980)Google Scholar
  7. 7.
    Rao, C.K., Mirza, S.: A note on vibrations of generally restrained beams. J. Sound Vib. 130, 453–465 (1989).  https://doi.org/10.1016/0022-460X(89)90069-2CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Lila Chalah-Rezgui
    • 1
  • Farid Chalah
    • 1
  • Salah Eddine Djellab
    • 1
  • Ammar Nechnech
    • 1
  • Abderrahim Bali
    • 2
  1. 1.Faculty of Civil EngineeringUsthbAlgiersAlgeria
  2. 2.Ecole Nationale PolytechniqueAlgiersAlgeria

Personalised recommendations