Periodic geometrically nonlinear free vibrations of circular plates

• Type: Article in International Scientific Journal
• Date: 2008

Authors

S. Stoykov (Author) FEUP; P. Ribeiro (Author) FEUP

Journal

Title: Journal of Sound and Vibration

Vol. 315

Pages: 536-555

ISSN: 0022-460X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 14 Citations

ISI Web of Science

Scopus - 17 Citations

INSPEC

COMPENDEX

Scientific classification

FOS: Engineering and technology > Mechanical engineering

CORDIS: Technological sciences > Engineering > Civil engineering > Structural engineering ; Technological sciences > Engineering > Mechanical engineering > Vibration engineering

Other information

Authenticus ID: P-003-WZ6

DOI: 10.1016/j.jsv.2008.02.001

Abstract (EN): The geometrically nonlinear free vibrations of thin isotropic circular plates are investigated using a multi-degree-of-freedom model, which is based on thin plate theory and on Von Karman's nonlinear strain-displacement relations. The middle plane in-plane displacements are included in the formulation and the common axisymmetry restriction is not imposed. The equations of motion are derived by the principle of the virtual work and an approximated model is achieved by assuming that the in-plane and transverse displacement fields are given by weighted series of spatial functions. These spatial functions are based on hierarchical sets of polynomials, which have been successfully used in p-version finite elements for beams and rectangular plates, and on trigonometric functions. Employing the harmonic balance method, the differential equations of motion are converted into a nonlinear algebraic form and then solved by a continuation method. Convergence with the number of shape functions and of harmonics is analysed. The numerical results obtained are presented and compared with available published results; it is shown that the hierarchical sets of functions provide good results with a small number of degrees of freedom. Internal resonances are found and the ensuing multimodal oscillations are described.

Language: English

Type (Professor's evaluation): Scientific