Skip to main content
SpringerLink
Log in

Free vibration analysis of elastically supported Timoshenko columns with attached masses by transfer matrix and finite element methods

  • Published:
Sadhana Aims and scope Submit manuscript

Abstract

This paper deals with the free vibration of Timoshenko columns with attached masses having rotary inertia. The support of the model is elastically restrained against rotation. The concept of fixity factor is used to define the stiffness of the elastic connection relative to that of the column. The governing equation of the column elements is solved by applying the separation of variables method in the transfer matrix method (TMM) algorithm. The same problems are solved, also, by finite element method (FEM) algorithm in which the matrices in equation of motion are obtained for Timoshenko column, and the results are compared with the ones of TMM. The comparison graphs are presented in numerical analysis to show the effectiveness of the considered methods, and it is resulted that FEM gives closer results to TMM.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bapat C N, Bapat C 1987 Natural Frequencies of a beam with non-classical boundary conditions and concentrated masses. J. Sound and Vibration 112: 177–182

    Article  Google Scholar 

  • Cabrero J M, Bayo E 2005 Development of practical design methods for steel structures with semirigid connections. Eng. Struct. 27: 1125–1137

    Article  Google Scholar 

  • Çatal H H 2005 Matrix methods in structural and earthquake engineering, 2. ed., Turkey, Dokuz Eylül University Engineering Faculty Editions 294: 249–251

    Google Scholar 

  • Demirdağg O 2005 Obtaining non-linear response spectrum of semi-rigid supported frames, Ph. D. Thesis, Dokuz Eylül University, Izmir, Turkey

    Google Scholar 

  • Esmailzadeh E, Ohadi A R 2000 Vibration and stability analysis of non-uniform Timoshenko beams under axial and distributed tangential loads. J. Sound and Vibration 236: 443–456

    Article  Google Scholar 

  • Ferreira A J M, Fasshauer G E 2006 Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method. Comput. Meth. Appl. Mech. and Eng. 196: 134–146

    Article  MATH  Google Scholar 

  • Gökdağ H, Kopmaz O 2005 Coupled bending and torsional vibration of a beam with in-span and tip attachments. J. Sound and Vibration 287: 591–610

    Google Scholar 

  • Hurty W C, Rubinstein M F 1964 Dynamics of structures, (India: Prentice Hall) 210–215

    Google Scholar 

  • Karami G, Malekzadeh P, Shahpari S A 2003 A DQEM for vibration of shear deformable non-uniforms beams with general boundary conditions. Eng. Struct. 25: 1169–1178

    Article  Google Scholar 

  • Lee U, Kim J, Oh H 2004 Spectral analysis for the transverse vibration of an axially moving Timoshenko beam. J. Sound and Vibration 271: 685–703

    Article  Google Scholar 

  • Lin H P, Chang S C 2005 Free vibration analysis of multi-span beams with intermediate flexible constraints. J. Sound and Vibration 281: 155–169

    Article  Google Scholar 

  • Low K H 1991 A comprehensive approach for the eigenproblem of beams with arbitrary boundary conditions. Comput. and Struct. 39: 671–678

    Article  Google Scholar 

  • Özkaya E 2002 Non-linear transverse vibrations of a simply supported beam carrying concentrated masses. J. Sound and Vibration 257: 413–424

    Article  Google Scholar 

  • Paz M 1997 Structural dynamics: Theory and computation (USA: Chapmann & Hall) 405–408

    Google Scholar 

  • Posiadala B 1997 Free vibrations of uniform Timoshenko beams with attachments. J. Sound and Vibration 204: 359–369

    Article  Google Scholar 

  • Przemieniecki J S 1968 Theory of matrix structural analysis USA: McGraw-Hill, Inc, 74–80 and 292–297

    MATH  Google Scholar 

  • Rao G V, Saheb K M, Janardhan G R 2006 Fundamental frequency for large amplitude vibrations of uniform Timoshenko beams with central point concentrated mass using coupled displacement field method. J. Sound and Vibration 298: 221–232

    Article  Google Scholar 

  • Ruta P 2006 The application of Chebyshev polynomials to the solution of the non-prismatic Timoshenko beam vibration problem. J. Sound and Vibration 296: 243–263

    Article  Google Scholar 

  • Salarieh H, Ghorashi M 2006 Free vibration of Timoshenko beam with finite mass rigid tip load and flexural-torsional coupling. Int. J. Mech. Sci. 48: 763–779

    Article  Google Scholar 

  • Thomson W T 1981 Theory of vibration with application, 2nd ed., (Englewood Cliffs: USA, Prentice-Hall, Inc.) 313–316

    Google Scholar 

  • Tuma J J, Cheng F Y 1983 Theory and problems of dynamic structural analysis: Schaum’s outline series USA: McGraw-Hill, Inc, 157

    Google Scholar 

  • Wu J J 2006 Use of equivalent mass method for free vibration analysis of a beam carrying multiple two-dof spring-mass systems with inertia effect of the helical springs considered. Int. J. Numer. Meth. Eng. 65: 653–678

    Article  MATH  Google Scholar 

  • Wu J S, Chen D W 2001 Free vibration analysis of a Timoshenko beam carrying multiple spring-mass systems by using the numerical assembly technique. Int. J. Numer. Meth. Eng. 50: 1039–1058

    Article  MATH  Google Scholar 

  • Wu J S, Chiang L K 2004 Free vibration of solid and hollow wedge beams with rectangular or circular cross-sections and carrying any number of point masses. Int. J. Numer. Meth. Eng. 60: 695–718

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Civil Engineering Department, Pamukkale University, Engineering Faculty, 20070, Kinikli Campus, Denizli, Turkey

    Oktay Demirdaǧ

Authors
  1. Oktay Demirdaǧ
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oktay Demirdaǧ.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Demirdaǧ, O. Free vibration analysis of elastically supported Timoshenko columns with attached masses by transfer matrix and finite element methods. Sadhana 33, 57–68 (2008). https://doi.org/10.1007/s12046-008-0005-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12046-008-0005-6

Keywords

Search

Navigation