Non-linear vibration of beams with internal resonance by the hierarchical finite-element method

• Type: Article in International Scientific Journal
• Date: 1999

Authors

Pedro Leal Ribeiro (Author) FEUP; Petyt, M (Author) Other

Journal

Title: Journal of Sound and Vibration

Vol. 224 No. 4

Pages: 591-624

ISSN: 0022-460X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 73 Citations

Scopus - 84 Citations

Other information

Authenticus ID: P-001-3TP

DOI: 10.1006/jsvi.1999.2193

Abstract (EN): The hierarchical finite-element (HFEM) and the harmonic balance methods (HBM) are used to investigate the geometrically non-linear free and steady-state forced vibrations of uniform, slender beams. The beam analogue of von Karman's non-linear strain-displacement relationships are employed and the middle plane in-plane displacements are included in the model. The equations of motion are developed by applying the principle of virtual work and are solved by a continuation method, 1:3 and 1:5 internal resonances are discovered and their consequences are discussed. The convergence properties of the HFEM are analyzed and it is demonstrated that the HFEM model requires far fewer degrees of freedom than the h-version of the FEM models presented in the Literature. (C) 1999 Academic Press.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 34