Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T08:41:08.338Z Has data issue: false hasContentIssue false
  • English
  • Français

Transfer Matrices for Beams Loaded Axially and Laid on an Elastic Foundation

Published online by Cambridge University Press:  07 June 2016

B. A. Djodjo
B. A. Djodjo*
Affiliation:
Institute of Technology, Serbian Academy of Sciences and Arts, Belgrade
Get access

Summary

Using a modified model of the axially-loaded Timoshenko beam, nine field transfer matrices for the homogeneous case and three field matrices for the non-homogeneous case have been derived, covering thus all the “cases of state” of continuous beams loaded axially and laid on an elastic foundation. The loads and restraints (translatory and rotatory) may be both concentrated and distributed. The matrices make possible a simultaneous treatment of free vibrations, forced vibrations, statics and buckling.

Type
Research Article
Information
Aeronautical Quarterly , Volume 20 , Issue 3 , August 1969 , pp. 281 - 306
Copyright
Copyright © Royal Aeronautical Society. 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Thomson, W. Matrix solution for the vibration of non-uniform beams. Journal of Applied Mechanics, September 1950.CrossRefGoogle Scholar
2. Pestel, E. Ein allgemeines Verfahren zur Berechnung freder und erzwungener Schwingungen von Stabwerken. Abhandlungen Braunschweiger Wissenschaftlicher Gesellschaft, Vol. 6, 1954.Google Scholar
3. Fuhrke, H. Bestimmung von Balkenschwingungen mit Hilfe des Matrizenkalküls. Ingenieur-Archiv, Vol. 23, 1955.Google Scholar
4. Falk, S. Die Berechnung des beliebig gesttitzten Durchlaufträgers nach dem Reduktions-verfahren. Ingenieur-Archiv, Vol. 24, 1956.CrossRefGoogle Scholar
5. Marguerre, K. Vibration and stability problems of beams treated by matrices. Journal of Mathematics and Physics, Vol. 35, 1956.Google Scholar
6. Fuhrke, H. Eigenwert-Bestimmung mit Hilfe von abgeleiteten Übertragungsmatrizen. VDI-Berichte Vol. 30, 1958.Google Scholar
7. Pestel, E., Schumpich, G. and Spierig, S. Katalog von Übertragungsmatrizen zur Berechnung technischer Schwingungsprobleme. VDI-Berichte, Vol. 35, 1959.Google Scholar
8. Pestel, E. C.and Leckie, F. A. Matrix methods in elastomechanics. McGraw-Hill, 1963.Google Scholar
9. Djodjo, B. A. On a method for calculating transverse vibrations, static deflections and buckling loads of beams. Recueil des Travaux de l’Institut de Constructions Mécaniques “Vladimir Farmakovski”, Vol. 10, 1964.Google Scholar
10. Timoshenko, S. and Young, D. Vibration problems in engineering, van Nostrand, 1955.Google Scholar
11. Biezeno, C. and Grammel, R. Engineering dynamics, Vol. III. Blackie, London, 1954.Google Scholar
12. Klotier, K. Technische Schwingungslehre. Zweiter Band. Springer, 1960.Google Scholar
13. Kolousek, V. Dynamika stavebnich konstrukci. Statni nakladatelstvi technicke literatury, 1956. (Translations: Calcul des efforts dynamiques dans les ossatures rigides, Dunod, Paris, 1959; Dynamik der Baukonstruktionen, Verlag für Bauwesen, 1962; Dinamika stroitel’nih konstrukcii, Izdatel’stvo literaturi po stroitel’stvu, 1965.)Google Scholar
14. Szidarovszky, J. Natural vibration of a bar under axial force, taking into consideration the effect of shearing force and rotatory inertia. Acta Technica Academiae Scientiarum Hungaricae, Vol. 34, 1962.Google Scholar
15. Timoshenko, S. Theory of elastic stability. McGraw-Hill, 1936.Google Scholar
16. Djodjo, B. A. On the buckling of the Timoshenko beam. Recueil des Travaux de l’Institut de Constructions Mécaniques “Vladimir Farmakovski”, Vol. 11, 1966.Google Scholar