In this work, nonlinear free vibrations of fully geometrically exact Timoshenko-Ehrenfest beams are investigated. First, the exact strong form of the Timonshenko-Ehrenfest beam, considering the geometrical nonlinearity, is derived, and the required formulations are obtained. Since the strong forms of governing equations are highly nonlinear, a nonlinear finite element analysis (FEA) is employed to obtain the weak form. The FEA is utilized to compute natural frequencies and mode shapes; the direct scheme is adopted to solve the eigenvalue problem which is obtained by eliminating nonlinear terms. Then, each eigenvector is normalized, and the nonlinear stiffness matrix is derived and the nonlinear free vibration analysis is carried out. A recursive procedure is adopted to proceed until the convergence criterion is satisfied. Finally, the applicability of the proposed formulation is provided with some examples and results are compared with those available in the literature.

Nonlinear free vibrations of Timoshenko–Ehrenfest beams using finite element analysis and direct scheme / Firouzi, Nasser; Lenci, Stefano; Amabili, Marco; Rabczuk, Timon. - In: NONLINEAR DYNAMICS. - ISSN 0924-090X. - STAMPA. - 112:9(2024), pp. 7199-7213. [10.1007/s11071-024-09403-3]

Nonlinear free vibrations of Timoshenko–Ehrenfest beams using finite element analysis and direct scheme

Lenci, Stefano
Secondo
;
2024-01-01

Abstract

In this work, nonlinear free vibrations of fully geometrically exact Timoshenko-Ehrenfest beams are investigated. First, the exact strong form of the Timonshenko-Ehrenfest beam, considering the geometrical nonlinearity, is derived, and the required formulations are obtained. Since the strong forms of governing equations are highly nonlinear, a nonlinear finite element analysis (FEA) is employed to obtain the weak form. The FEA is utilized to compute natural frequencies and mode shapes; the direct scheme is adopted to solve the eigenvalue problem which is obtained by eliminating nonlinear terms. Then, each eigenvector is normalized, and the nonlinear stiffness matrix is derived and the nonlinear free vibration analysis is carried out. A recursive procedure is adopted to proceed until the convergence criterion is satisfied. Finally, the applicability of the proposed formulation is provided with some examples and results are compared with those available in the literature.
2024
File in questo prodotto:
File Dimensione Formato  
Firouzi_Nonlinear-free-vibrations-Timoshenko-Ehrenfest_2024.pdf

Solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza d'uso: Tutti i diritti riservati
Dimensione 505.13 kB
Formato Adobe PDF
505.13 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Firouzi_Nonlinear-free-vibrations-Timoshenko_Post-print_2024.pdf

embargo fino al 13/03/2025

Descrizione: This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://dx.doi.org/10.1007/s11071-024-09403-3
Tipologia: Documento in post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza d'uso: Licenza specifica dell’editore
Dimensione 313.89 kB
Formato Adobe PDF
313.89 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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: https://hdl.handle.net/11566/328660
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 4
social impact