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Vibration of shear‐deformable rectangular plates using a spline‐function Rayleigh‐Ritz approach
Author(s) -
Wang S.,
Dawe D. J.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620360409
Subject(s) - rayleigh–ritz method , orthotropic material , deflection (physics) , vibration , mathematics , spline (mechanical) , ritz method , mathematical analysis , geometry , shear (geology) , rayleigh scattering , plate theory , structural engineering , materials science , engineering , physics , boundary value problem , classical mechanics , finite element method , optics , acoustics , composite material
The prediction of the natural frequencies of vibration of rectangular plates or orthotropic laminates is described, through the use of B‐spline functions as trial functions in a Rayleigh‐Ritz approach. Through‐thickness shear deformation effects are included in the analysis and hence assumptions have to be made for the spatial variation over the plate middle surface of each of the lateral deflection and the two rotation components. Two versions of the spline‐function Rayleigh‐Ritz approach are described: in one of these the deflection and rotations are represented by functions of the same polynomial order, whilst in the other a lower‐order representation is used for each rotation component in one of the co‐ordinate directions. It is shown in a number of applications that the former version leads to shear‐locking behaviour whilst the latter version avoids this behaviour and is suitable for the analysis of both thick and thin plates.