Investigation of surface effects on the natural frequency of a functionally graded cylindrical nanoshell based on nonloc
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Investigation of surface effects on the natural frequency of a functionally graded cylindrical nanoshell based on nonlocal strain gradient theory Khashayar Ghorbani, Ali Rajabpoura
, Majid Ghadirib , Zahra Keshtkar
Advanced Simulation and Computing Laboratory (ASCL), Mechanical Engineering Department, Imam Khomeini International University, Qazvin 34149-16818, Iran Received: 6 January 2020 / Accepted: 25 August 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In submicron structures, because of surface and small-scale effects, the classical continuum theory does not lead to accurate results. In order to use this method in the study of the mechanical behavior of such structures, surface elasticity and size-dependent theories have been introduced. In this paper, by simultaneously applying the theories of Gurtin–Murdoch surface elasticity and the nonlocal strain gradient, the vibration behavior of a functionally graded nanoshell has been investigated. To this end, the governing motion equations and related boundary conditions are extracted utilizing Hamilton’s principle and the first-order shear deformation theory of shell and then will be solved by the generalized differential quadrature method. The effects of surface properties such as surface elastic properties, residual surface stress, and surface mass density have been studied. Also, a comparative study between different continuum mechanics theories, with and without surface effects, at different boundary conditions and values of length-to-radius ratio and FG gradient index is presented.
1 Introduction Due to the wide range of advanced engineering applications of nonhomogeneous submicron structures, studying the various aspects of their characteristics is of the great importance in modern engineering. Besides the experimental and atomistic modeling methods which have difficulties to perform and are computationally expensive, the continuum mechanicsbased approach provides an acceptable and dominant method in this regard. The classical continuum theory due to lack of consideration the two important characteristics of submicron structures, called surface and small-scale effects, is not able to estimate an accurate response of such structures. In submicron structures, the equilibrium conditions of atoms in exposure to a free surface are different from those inside since the surface-to-volume ratio is high. In other words, the energy of surface atoms is different from the bulk atoms. This feature that is known as surface effects is a significant factor in the investigation of submicron structures. In order to
a e-mail: [email protected] (corresponding author) b e-mail: [email protected] (corresponding author)
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incorporate the surface effects into the mechanical analysis of submicron structures using the continuum mechanics-based approach, Gurtin and Murdoch [1, 2] presented the surface elasticity theory. On the b
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