Open Access

ARTICLE

Exact Elasticity Solution for Natural Frequencies of Functionally Graded Simply-supported Structures

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1 Corresponding author: Salvatore Brischetto, Assistant Professor, Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, ITALY.
Tel: +39.011.090.6813; Fax: +39.011.090.6899; Email: salvatore.brischetto@polito.it.

Computer Modeling in Engineering & Sciences 2013, 95(5), 391-430. https://doi.org/10.3970/cmes.2013.095.391

Abstract

This paper gives an exact three-dimensional elastic model for the free vibration analysis of functionally graded one-layered and sandwich simply-supported plates and shells. An exact elasticity solution is proposed for the differential equations of equilibrium written in general orthogonal curvilinear coordinates. The equations consider a geometry for shells without simplifications, and allow the analysis of the cases of spherical shell panels, cylindrical shell panels, cylindrical closed shells and plates. The main novelty is the possibility of a general formulation for these geometries. The coefficients in equilibrium equations depend on the thickness coordinate because of the radii of curvature for the shell geometries and/or the use of functionally graded layers. These equations are solved in a layer-wise form by introducing a number of mathematical layers where the coefficients are constant. An exhaustive 3D overview of the vibration modes is given for a number of thickness ratios, imposed wave numbers, geometries and embedded materials. Results are given for one-layered functionally graded plates and shells and for sandwich structures with external homogenous skins and an internal core made of functionally graded material. These results can also be used as reference solutions for the validation of analytical or numerical two-dimensional models for functionally graded plates and shells.

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