The problem of free vibrations of the Timoshenko beam model has been addressed in the first part of this paper. A careful analysis of the governing equations has shown that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. Here, as an extension, the case of a doubly clamped beam is considered. For both parts of the spectrum, the values of natural frequencies are computed and the expressions of eigenmodes are provided: this allows to acknowledge that the nature of vibration modes changes when moving across the transition frequency. This case is a meaningful example of more general ones, where the wave-numbers equation cannot be written in a factorized form and hence must be solved by general rootfinding methods for nonlinear transcendental equations. These theoretical results can be used as further benchmarks for assessing the correctness of the numerical values provided by several numerical techniques, e.g. finite element models.

On the whole spectrum of Timoshenko beams. Part II: Further applications

CAZZANI, ANTONIO MARIA;STOCHINO, FLAVIO;
2016

Abstract

The problem of free vibrations of the Timoshenko beam model has been addressed in the first part of this paper. A careful analysis of the governing equations has shown that the vibration spectrum consists of two parts, separated by a transition frequency, which, depending on the applied boundary conditions, might be itself part of the spectrum. Here, as an extension, the case of a doubly clamped beam is considered. For both parts of the spectrum, the values of natural frequencies are computed and the expressions of eigenmodes are provided: this allows to acknowledge that the nature of vibration modes changes when moving across the transition frequency. This case is a meaningful example of more general ones, where the wave-numbers equation cannot be written in a factorized form and hence must be solved by general rootfinding methods for nonlinear transcendental equations. These theoretical results can be used as further benchmarks for assessing the correctness of the numerical values provided by several numerical techniques, e.g. finite element models.
Frequency spectrum; Structural dynamics; Timoshenko beam; Vibration analysis; Mathematics (all); Physics and Astronomy (all); Applied Mathematics
File in questo prodotto:
File Dimensione Formato  
ZAMP_67_(2)_2016_#25_1-21.pdf

Solo gestori archivio

Descrizione: ZAMP_67_(2)_2016_#25_1-21
Tipologia: versione editoriale
Dimensione 1.44 MB
Formato Adobe PDF
1.44 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
ZAMP_2_hdl_11584_195897.pdf

accesso aperto

Descrizione: Versione Open Access
Tipologia: versione pre-print
Dimensione 1.36 MB
Formato Adobe PDF
1.36 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/195897
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 40
  • ???jsp.display-item.citation.isi??? 18
social impact