Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders

Salvatore Brischetto; Roberto Torre

Curved and Layered Structures (2014)

  • Volume: 1, Issue: 1
  • ISSN: 2353-7396

Abstract

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The paper proposes a comparison between classical two-dimensional (2D) finite elements (FEs) and an exact three-dimensional (3D) solution for the free vibration analysis of one-layered and multilayered isotropic, composite and sandwich plates and cylinders. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the finite element method and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 2D finite element results are obtained by means of a well-known commercial FE code. The differences between 2D FE solutions and 3D exact solutions depend on the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.

How to cite

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Salvatore Brischetto, and Roberto Torre. "Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders." Curved and Layered Structures 1.1 (2014): null. <http://eudml.org/doc/276963>.

@article{SalvatoreBrischetto2014,
abstract = {The paper proposes a comparison between classical two-dimensional (2D) finite elements (FEs) and an exact three-dimensional (3D) solution for the free vibration analysis of one-layered and multilayered isotropic, composite and sandwich plates and cylinders. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the finite element method and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 2D finite element results are obtained by means of a well-known commercial FE code. The differences between 2D FE solutions and 3D exact solutions depend on the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.},
author = {Salvatore Brischetto, Roberto Torre},
journal = {Curved and Layered Structures},
keywords = {plates; shells; finite element method; exact three-dimensional solution; free vibrations; vibration modes},
language = {eng},
number = {1},
pages = {null},
title = {Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders},
url = {http://eudml.org/doc/276963},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Salvatore Brischetto
AU - Roberto Torre
TI - Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders
JO - Curved and Layered Structures
PY - 2014
VL - 1
IS - 1
SP - null
AB - The paper proposes a comparison between classical two-dimensional (2D) finite elements (FEs) and an exact three-dimensional (3D) solution for the free vibration analysis of one-layered and multilayered isotropic, composite and sandwich plates and cylinders. Low and high order frequencies are analyzed for thick and thin simply supported structures. Vibration modes are investigated to make a comparison between results obtained via the finite element method and those obtained by means of the exact three-dimensional solution. The 3D exact solution is based on the differential equations of equilibrium written in general orthogonal curvilinear coordinates. This exact method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structure. The geometry for shells is considered without any simplifications. The 2D finite element results are obtained by means of a well-known commercial FE code. The differences between 2D FE solutions and 3D exact solutions depend on the considered mode, the order of frequency, the thickness ratio of the structure, the geometry, the embedded material and the lamination sequence.
LA - eng
KW - plates; shells; finite element method; exact three-dimensional solution; free vibrations; vibration modes
UR - http://eudml.org/doc/276963
ER -

References

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