Free Vibration Analysis of a Functionally Graded Cylindrical Nanoshell Surrounded by Elastic Foundation Based on the Modified Couple Stress Theory

Document Type : Research Article

Authors

Department of Mechanical Engineering, Imam Khomeini International University, Qazvin, Iran

Abstract

In this article, free vibration analysis of functionally graded cylindrical nanoshell on
the basis of the modified couple stress theory is investigated. The nanoshell is embedded in an elastic
Pasternak medium, which is obtained by adding a shear layer to the Winkler model. In addition, the
boundary conditions at two ends of cylindrical nanoshell are simply supported. It is assumed that the
functionally graded cylindrical nanoshell, is made of aluminum and ceramic, follows the volume fraction
definition and law of mixtures, and its properties change as a power function through its thickness.
Governing equations and boundary conditions are obtained by applying the Hamilton’s principle and are
based on first-order shear deformation. Navier solution is used for predicting the natural frequencies of
functionally graded cylindrical nanoshell. Finally, the effect of parameters such as material length scale,
circumferential wave number, the length to radius ratio, shear correction factor, power low index and
elastic foundation coefficients of Winkler and Pasternak on natural frequency of functionally graded
cylindrical nanoshell are identified. The results show, there is a very good agreement between the results
of molecular dynamics simulations by previous researchers with the results of this study.

Keywords

Main Subjects

References

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Amirkabir Journal of Mechanical Engineering
Volume 49, Issue 4
March 2018
Pages 721-730

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