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Archive of Applied Mechanics
Erschienen in: Archive of Applied Mechanics 4/2020

22.11.2019 | Original

Dynamics of vibrating beams using first-order theory based on Legendre polynomial expansion

verfasst von: A. Czekanski, V. V. Zozulya

Erschienen in: Archive of Applied Mechanics | Ausgabe 4/2020

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Abstract

First-order models are used in the analysis of the tension–compression and transverse bending modes of beam vibration. The equation of motion for each mode and the expressions for boundary conditions are obtained using the generalized variational principle. Systems of partial differential equations for the longitudinal and bending modes of vibrating beams are reduced to a single fourth-order equation, and frequency equations are obtained. The problem of free and forced vibrations of beams that are simply supported at both ends is presented. An analysis and comparison with well-known theories is performed using computer algebra system Mathematica.
Vorheriger Artikel A vehicle–track beam matching index in EMS maglev transportation system
Nächster Artikel Saint-Venant torsion of non-homogeneous orthotropic circular cylinder

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Metadaten
Titel
Dynamics of vibrating beams using first-order theory based on Legendre polynomial expansion
verfasst von
A. Czekanski
V. V. Zozulya
Publikationsdatum
22.11.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Archive of Applied Mechanics / Ausgabe 4/2020
Print ISSN: 0939-1533
Elektronische ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-019-01639-5

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