R-functions theory applied to investigation of nonlinear free vibrations of functionally graded shallow shells
R-functions theory applied to investigation of nonlinear free vibrations of functionally graded shallow shells
Nonlinear free vibration of functionally graded shallow shells with complex planform is investigated using the R-functions method (RFM) and variational Ritz method. The proposed method is developed in the framework of the first–order shear deformation shallow shell theory (FSDT). Effect of transverse shear strains and rotary inertia are taken into account. The properties of functionally graded materials (FGM) are assumed to be varying continuously through the thickness according to a power law distribution. The Rayleigh-Ritz procedure is applied to obtain the frequency equation. Admissible functions are constructed by the R-functions theory. To implement the proposed approach the corresponding software has been developed. Comprehensive numerical results for three types of shallow shells with positive, zero and negative curvature with complex planform are presented in tabular and graphical forms. The convergence of the natural frequencies with increasing number of admissible functions has been checked out. Effect of volume fraction exponent, geometry of a shape and boundary conditions on the natural and nonlinear frequencies is brought out. For simply supported rectangular FG shallow shells, the results obtained are compared with those available in the literature. Comparison demonstrates a good accuracy of the approach proposed.
189-204
Shmatko, Tetyana
ea8e215f-ae8e-469c-a0d8-ca9bf9bca642
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
July 2018
Shmatko, Tetyana
ea8e215f-ae8e-469c-a0d8-ca9bf9bca642
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Shmatko, Tetyana and Bhaskar, Atul
(2018)
R-functions theory applied to investigation of nonlinear free vibrations of functionally graded shallow shells.
Nonlinear Dynamics, 93 (1), .
(doi:10.1007/s11071-017-3922-2).
Abstract
Nonlinear free vibration of functionally graded shallow shells with complex planform is investigated using the R-functions method (RFM) and variational Ritz method. The proposed method is developed in the framework of the first–order shear deformation shallow shell theory (FSDT). Effect of transverse shear strains and rotary inertia are taken into account. The properties of functionally graded materials (FGM) are assumed to be varying continuously through the thickness according to a power law distribution. The Rayleigh-Ritz procedure is applied to obtain the frequency equation. Admissible functions are constructed by the R-functions theory. To implement the proposed approach the corresponding software has been developed. Comprehensive numerical results for three types of shallow shells with positive, zero and negative curvature with complex planform are presented in tabular and graphical forms. The convergence of the natural frequencies with increasing number of admissible functions has been checked out. Effect of volume fraction exponent, geometry of a shape and boundary conditions on the natural and nonlinear frequencies is brought out. For simply supported rectangular FG shallow shells, the results obtained are compared with those available in the literature. Comparison demonstrates a good accuracy of the approach proposed.
Text
Journal_ND_Shmatko_Bhaskar_modified
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Accepted/In Press date: 3 November 2017
e-pub ahead of print date: 13 November 2017
Published date: July 2018
Identifiers
Local EPrints ID: 415607
URI: http://eprints.soton.ac.uk/id/eprint/415607
ISSN: 0924-090X
PURE UUID: f3d4f55d-a1cc-4efe-9d59-1861b0ec5364
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Date deposited: 16 Nov 2017 17:30
Last modified: 16 Mar 2024 05:56
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Author:
Tetyana Shmatko
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