Non-linear vibrations of deep cylindrical shells by the p-version finite element method

Article type: Research Article

Authors: Ribeiro, Pedro | Cochelin, Bruno | Bellizzi, Sergio

Affiliations: IDMEC/DEMEGI, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal | Laboratoire de Mécanique et d'Acoustique, CNRS, 31 chemin Joseph Aiguier, 13402 Marseille, France

Note: [] Corresponding author. Tel.: +351 22 508 17 16; Fax: +351 22 508 14 45; E-mail: [email protected]

Abstract: A p-version shell finite element based on the so-called shallow shell theory is for the first time employed to study vibrations of deep cylindrical shells. The finite element formulation for deep shells is presented and the linear natural frequencies of different shells, with various boundary conditions, are computed. These linear natural frequencies are compared with published results and with results obtained using a commercial software finite element package; good agreement is found. External forces are applied and the displacements in the geometrically non-linear regime computed with the p-model are found to be close to the ones computed using a commercial FE package. In all numerical tests the p-FE model requires far fewer degrees of freedom than the regular FE models. A numerical study on the dynamic behaviour of deep shells is finally carried out.

Keywords: Deep shells, p-version finite element method, geometrically non-linear vibrations

DOI: 10.3233/SAV-2010-0495

Journal: Shock and Vibration, vol. 17, no. 1, pp. 21-37, 2010