Eigenfrequency analysis of completely free multilayered rectangular plates using a higher-order model and Ritz technique

A numerical model for the analysis of the free vibration of multilayered, fully free rectangular plates with arbitrary layups is proposed. The model is based on a displacement field that assumes a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate and a tra...

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Bibliographic Details
Published in:Mechanics of composite materials and structures 1998-01, Vol.5 (1), p.55-80
Main Authors: Mota Soares, C M, dos Santos, J V A, Araujo, A L
Format: Article
Language:English
Online Access:Get full text
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Summary:A numerical model for the analysis of the free vibration of multilayered, fully free rectangular plates with arbitrary layups is proposed. The model is based on a displacement field that assumes a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate and a transverse displacement that is constant through the plate thickness. The displacement field accounts for a parabolic distribution of the transverse shear strains and satisfies the condition of zero transverse shear stresses on the top and bottom surfaces of the plate. The mathematical problem is solved by the Ritz technique, which relies on the minimization of the maximum Lagrangian functional, using a displacement field defined by beam functions in the form of finite series with undetermined parameters. The required mathematical operations for the development of the eigenvalue problem are carried out by symbolic manipulation. By deleting the higher-order terms of Reddy's displacement field or assuming the Love-Kirchhoff hypothesis, the first-order shear deformation and the classical plate theory models, respectively, are also obtained. These models are used to analyze several laminated composite plate problems, and the eigenfrequency results are compared among them and with alternative solutions.
ISSN:1075-9417