Bending, buckling and vibration of small-scale tapered beams

In this paper, a comprehensive study on mechanical behavior of non-uniform small scale beams in the framework of nonlocal strain gradient theory is presented. The governing equations and boundary conditions have been developed using Hamilton's principle and solved with the aid of finite element...

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Bibliographic Details
Published in:International journal of engineering science 2017-11, Vol.120, p.172-188
Main Authors: Rajasekaran, Sundaramoorthy, Khaniki, Hossein Bakhshi
Format: Article
Language:English
Subjects:
Beams (structural)
Bending
Boundary conditions
Buckling
Cross-sections
Deformation
Finite element
Finite element analysis
Finite element method
Free vibration
Hamilton's principle
Mechanical properties
Model accuracy
Nonlocal strain gradient
Strain
Studies
Tapered beam
Thickness
Variable cross section
Vibration
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Summary:In this paper, a comprehensive study on mechanical behavior of non-uniform small scale beams in the framework of nonlocal strain gradient theory is presented. The governing equations and boundary conditions have been developed using Hamilton's principle and solved with the aid of finite element method for introducing the bending, buckling and free vibration response of nano-beams. The current formulation could be used for all types of non-uniformities by varying the width and thickness of nano-beams along the length. The accuracy of the current model and formulation is verified by comparing the results with previous literature and those obtained by analytically solving simplified problems. In order to understand the influence of having non-uniform cross section on static and dynamic behavior of small scale beams, parametric study is presented and the effects of different parameters such as non-uniformity, non-local and strain gradient terms on natural frequency, buckling load and deformation are observed and discussed. It is seen that having non-uniform cross section in nonlocal strain gradient beams could lead to significant changes in mechanical behavior of such structures.
ISSN:0020-7225
1879-2197
DOI:10.1016/j.ijengsci.2017.08.005