Vibration of quadrilateral embedded multilayered graphene sheets based on nonlocal continuum models using the Galerkin method

Free vibration analysis of quadrilateral multilayered graphene sheets（MLGS） embedded in polymer matrix is carried out employing nonlocal continuum mechanics.The principle of virtual work is employed to derive the equations of motion.The Galerkin method in conjunction with the natural coordinates of...

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Bibliographic Details
Published in:Acta mechanica Sinica 2011-12, Vol.27 (6), p.967-976
Main Authors: Babaei, H., Shahidi, A. R.
Format: Article
Language:English
Subjects:
Classical and Continuum Physics
Computational Intelligence
Elastic modulus
Engineering
Engineering Fluid Dynamics
Galerkin methods
Galerkin方法
Graphene
Mathematical models
Nanomaterials
Nanostructure
Quadrilaterals
Research Paper
Theoretical and Applied Mechanics
Vibration
内嵌
四边形
模型
石墨薄片
聚合物基体
自由振动
非局部
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Summary:Free vibration analysis of quadrilateral multilayered graphene sheets（MLGS） embedded in polymer matrix is carried out employing nonlocal continuum mechanics.The principle of virtual work is employed to derive the equations of motion.The Galerkin method in conjunction with the natural coordinates of the nanoplate is used as a basis for the analysis.The dependence of small scale effect on thickness,elastic modulus,polymer matrix stiffness and interaction coefficient between two adjacent sheets is illustrated.The non-dimensional natural frequencies of skew,rhombic,trapezoidal and rectangular MLGS are obtained with various geometrical parameters and mode numbers taken into account,and for each case the effects of the small length scale are investigated.
ISSN:0567-7718
1614-3116
DOI:10.1007/s10409-011-0514-0