Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher-Order Hierarchical Beam Element
A higher-order finite beam element for free and forced vibration analysis of functionally graded Timoshenko beams in thermal environment is formulated by using hierarchical functions to interpolate the kinematic variables. The shear strain is constrained to constant to improve the efficiency of the...
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Hindawi Limited
2017-01-01
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2017/7025750 |
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doaj-89c36f0f732948adb938725c58599b572020-11-25T01:42:41ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472017-01-01201710.1155/2017/70257507025750Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher-Order Hierarchical Beam ElementDinh Kien Nguyen0Van Tuyen Bui1Institute of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, VietnamGraduate University of Science and Technology, VAST, 18 Hoang Quoc Viet, Hanoi, VietnamA higher-order finite beam element for free and forced vibration analysis of functionally graded Timoshenko beams in thermal environment is formulated by using hierarchical functions to interpolate the kinematic variables. The shear strain is constrained to constant to improve the efficiency of the element. The effect of environmental temperature is taken into account in the element derivation by considering that the material properties are temperature-dependent and the temperature is nonlinear distribution in the beam thickness. The accuracy of the derived formulation is confirmed by comparing the results obtained in the present work with the published data. Numerical investigations show that the formulated element is efficient, and it is capable of giving accurate vibration characteristics by a small number of elements. A parametric study is carried out to highlight the effect of the material inhomogeneity, temperature rise, and loading parameter on the dynamic behaviour of the beams. The influence of the aspect ratio on the dynamic behaviour of the beam is also examined and highlighted.http://dx.doi.org/10.1155/2017/7025750 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Dinh Kien Nguyen Van Tuyen Bui |
spellingShingle |
Dinh Kien Nguyen Van Tuyen Bui Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher-Order Hierarchical Beam Element Mathematical Problems in Engineering |
author_facet |
Dinh Kien Nguyen Van Tuyen Bui |
author_sort |
Dinh Kien Nguyen |
title |
Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher-Order Hierarchical Beam Element |
title_short |
Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher-Order Hierarchical Beam Element |
title_full |
Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher-Order Hierarchical Beam Element |
title_fullStr |
Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher-Order Hierarchical Beam Element |
title_full_unstemmed |
Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher-Order Hierarchical Beam Element |
title_sort |
dynamic analysis of functionally graded timoshenko beams in thermal environment using a higher-order hierarchical beam element |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2017-01-01 |
description |
A higher-order finite beam element for free and forced vibration analysis of functionally graded Timoshenko beams in thermal environment is formulated by using hierarchical functions to interpolate the kinematic variables. The shear strain is constrained to constant to improve the efficiency of the element. The effect of environmental temperature is taken into account in the element derivation by considering that the material properties are temperature-dependent and the temperature is nonlinear distribution in the beam thickness. The accuracy of the derived formulation is confirmed by comparing the results obtained in the present work with the published data. Numerical investigations show that the formulated element is efficient, and it is capable of giving accurate vibration characteristics by a small number of elements. A parametric study is carried out to highlight the effect of the material inhomogeneity, temperature rise, and loading parameter on the dynamic behaviour of the beams. The influence of the aspect ratio on the dynamic behaviour of the beam is also examined and highlighted. |
url |
http://dx.doi.org/10.1155/2017/7025750 |
work_keys_str_mv |
AT dinhkiennguyen dynamicanalysisoffunctionallygradedtimoshenkobeamsinthermalenvironmentusingahigherorderhierarchicalbeamelement AT vantuyenbui dynamicanalysisoffunctionallygradedtimoshenkobeamsinthermalenvironmentusingahigherorderhierarchicalbeamelement |
_version_ |
1725034851436855296 |