Eur. Phys. J. Plus (2020) 135: 103
https://doi.org/10.1140/epjp/s13360-019-00079-y

Regular Article

Novel study on functionally graded anisotropic doubly curved nanoshells

¹ Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
² Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Sidi Bel Abbès, Algeria

^* e-mail: behrouz.karami@miau.ac.ir

Received: 13 December 2018
Accepted: 9 October 2019
Published online: 23 January 2020

Abstract

This work aims at investigating the dispersion of elastic eaves in doubly curved nanoshells. The nonlocal strain gradient theory is adopted in conjunction with a higher-order shear deformation shell theory, to include the size-dependent effects. The nanoshells are made of functionally graded anisotropic materials, whose properties are changed exponentially through the thickness direction. Hamilton’s principle is employed to obtain the governing equations of wave motion which are solved analytically to compute the wave frequencies as well as phase velocities as a function of the wave number. The sensitivity of the wave response is analyzed for the exponential factor, small-scale parameters, geometrical conditions as well as wave number. In addition, the accuracy of modeling the nanoshells with less elastic coefficients compared to the anisotropic model is studied to disregard any kind of complex equations.