Buckling and Vibration of Functionally Graded Non-uniform Circular Plates Resting on Winkler Foundation
Abstract An investigation on the effect of uniform tensile in-plane force on the radially symmetric vibratory characteristics of functionally graded circular plates of linearly varying thickness along radial direction and resting on a Winkler foundation has been carried out on the basis of classical...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
Marcílio Alves
|
Series: | Latin American Journal of Solids and Structures |
Subjects: | |
Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252015001202231&lng=en&tlng=en |
id |
doaj-2bc72e1e707341248574d91b5641364e |
---|---|
record_format |
Article |
spelling |
doaj-2bc72e1e707341248574d91b5641364e2020-11-24T22:14:29ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-782512122231225810.1590/1679-78251595S1679-78252015001202231Buckling and Vibration of Functionally Graded Non-uniform Circular Plates Resting on Winkler FoundationRoshan LalNeha AhlawatAbstract An investigation on the effect of uniform tensile in-plane force on the radially symmetric vibratory characteristics of functionally graded circular plates of linearly varying thickness along radial direction and resting on a Winkler foundation has been carried out on the basis of classical plate theory. The non-homogeneous mechanical properties of the plate are assumed to be graded through the thickness and described by a power function of the thickness coordinate. The governing differential equation for such a plate model has been obtained using Hamilton's principle. The differential transform method has been employed to obtain the frequency equations for simply supported and clamped boundary conditions. The effect of various parameters like volume fraction index, taper parameter, foundation parameter and the in-plane force parameter has been analysed on the first three natural frequencies of vibration. By allowing the frequency to approach zero, the critical buckling loads for both the plates have been computed. Three-dimensional mode shapes for specified plates have been plotted. Comparison with existing results has been made.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252015001202231&lng=en&tlng=enFunctionally graded circular platesBucklingDifferential transformWinkler foundation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Roshan Lal Neha Ahlawat |
spellingShingle |
Roshan Lal Neha Ahlawat Buckling and Vibration of Functionally Graded Non-uniform Circular Plates Resting on Winkler Foundation Latin American Journal of Solids and Structures Functionally graded circular plates Buckling Differential transform Winkler foundation |
author_facet |
Roshan Lal Neha Ahlawat |
author_sort |
Roshan Lal |
title |
Buckling and Vibration of Functionally Graded Non-uniform Circular Plates Resting on Winkler Foundation |
title_short |
Buckling and Vibration of Functionally Graded Non-uniform Circular Plates Resting on Winkler Foundation |
title_full |
Buckling and Vibration of Functionally Graded Non-uniform Circular Plates Resting on Winkler Foundation |
title_fullStr |
Buckling and Vibration of Functionally Graded Non-uniform Circular Plates Resting on Winkler Foundation |
title_full_unstemmed |
Buckling and Vibration of Functionally Graded Non-uniform Circular Plates Resting on Winkler Foundation |
title_sort |
buckling and vibration of functionally graded non-uniform circular plates resting on winkler foundation |
publisher |
Marcílio Alves |
series |
Latin American Journal of Solids and Structures |
issn |
1679-7825 |
description |
Abstract An investigation on the effect of uniform tensile in-plane force on the radially symmetric vibratory characteristics of functionally graded circular plates of linearly varying thickness along radial direction and resting on a Winkler foundation has been carried out on the basis of classical plate theory. The non-homogeneous mechanical properties of the plate are assumed to be graded through the thickness and described by a power function of the thickness coordinate. The governing differential equation for such a plate model has been obtained using Hamilton's principle. The differential transform method has been employed to obtain the frequency equations for simply supported and clamped boundary conditions. The effect of various parameters like volume fraction index, taper parameter, foundation parameter and the in-plane force parameter has been analysed on the first three natural frequencies of vibration. By allowing the frequency to approach zero, the critical buckling loads for both the plates have been computed. Three-dimensional mode shapes for specified plates have been plotted. Comparison with existing results has been made. |
topic |
Functionally graded circular plates Buckling Differential transform Winkler foundation |
url |
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252015001202231&lng=en&tlng=en |
work_keys_str_mv |
AT roshanlal bucklingandvibrationoffunctionallygradednonuniformcircularplatesrestingonwinklerfoundation AT nehaahlawat bucklingandvibrationoffunctionallygradednonuniformcircularplatesrestingonwinklerfoundation |
_version_ |
1725798628910432256 |