Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 49 4 2018 02 20 Free Vibration Analysis of a Functionally Graded Cylindrical Nanoshell Surrounded by Elastic Foundation Based on the Modified Couple Stress Theory Free Vibration Analysis of a Functionally Graded Cylindrical Nanoshell Surrounded by Elastic Foundation Based on the Modified Couple Stress Theory 721 730 802 10.22060/mej.2016.802 FA M. Ghadiri Department of Mechanical Engineering, Imam Khomeini International University, Qazvin, Iran H. Safarpour Department of Mechanical Engineering, Imam Khomeini International University, Qazvin, Iran Journal Article 2015 12 06 In this article, free vibration analysis of functionally graded cylindrical nanoshell on<br />the basis of the modified couple stress theory is investigated. The nanoshell is embedded in an elastic<br />Pasternak medium, which is obtained by adding a shear layer to the Winkler model. In addition, the<br />boundary conditions at two ends of cylindrical nanoshell are simply supported. It is assumed that the<br />functionally graded cylindrical nanoshell, is made of aluminum and ceramic, follows the volume fraction<br />definition and law of mixtures, and its properties change as a power function through its thickness.<br />Governing equations and boundary conditions are obtained by applying the Hamilton’s principle and are<br />based on first-order shear deformation. Navier solution is used for predicting the natural frequencies of<br />functionally graded cylindrical nanoshell. Finally, the effect of parameters such as material length scale,<br />circumferential wave number, the length to radius ratio, shear correction factor, power low index and<br />elastic foundation coefficients of Winkler and Pasternak on natural frequency of functionally graded<br />cylindrical nanoshell are identified. The results show, there is a very good agreement between the results<br />of molecular dynamics simulations by previous researchers with the results of this study. In this article, free vibration analysis of functionally graded cylindrical nanoshell on<br />the basis of the modified couple stress theory is investigated. The nanoshell is embedded in an elastic<br />Pasternak medium, which is obtained by adding a shear layer to the Winkler model. In addition, the<br />boundary conditions at two ends of cylindrical nanoshell are simply supported. It is assumed that the<br />functionally graded cylindrical nanoshell, is made of aluminum and ceramic, follows the volume fraction<br />definition and law of mixtures, and its properties change as a power function through its thickness.<br />Governing equations and boundary conditions are obtained by applying the Hamilton’s principle and are<br />based on first-order shear deformation. Navier solution is used for predicting the natural frequencies of<br />functionally graded cylindrical nanoshell. Finally, the effect of parameters such as material length scale,<br />circumferential wave number, the length to radius ratio, shear correction factor, power low index and<br />elastic foundation coefficients of Winkler and Pasternak on natural frequency of functionally graded<br />cylindrical nanoshell are identified. The results show, there is a very good agreement between the results<br />of molecular dynamics simulations by previous researchers with the results of this study. https://mej.aut.ac.ir/article_802_1141938ba2c2b13f5505d7c424ebae5f.pdf