The University of Southampton
University of Southampton Institutional Repository

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
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.
0924-090X
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Shmatko, Tetyana
ea8e215f-ae8e-469c-a0d8-ca9bf9bca642
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Shmatko, Tetyana
ea8e215f-ae8e-469c-a0d8-ca9bf9bca642

Bhaskar, Atul and Shmatko, Tetyana (2017) R-functions theory applied to investigation of nonlinear free vibrations of functionally graded shallow shells. Nonlinear Dynamics. (doi:10.1007/s11071-017-3922-2).

Record type: Article

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 - Accepted Manuscript
Restricted to Repository staff only until 13 November 2018.
Request a copy

More information

Accepted/In Press date: 3 November 2017
e-pub ahead of print date: 13 November 2017

Identifiers

Local EPrints ID: 415607
URI: https://eprints.soton.ac.uk/id/eprint/415607
ISSN: 0924-090X
PURE UUID: f3d4f55d-a1cc-4efe-9d59-1861b0ec5364

Catalogue record

Date deposited: 16 Nov 2017 17:30
Last modified: 19 Jul 2019 17:50

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×