Analytical Procedure for Determining Natural Frequencies of Annular Single-Layered Graphene Sheet via Nonlocal Elasticity Theory

作者：Moshir Saeed Khadem^*; Eipakchi Hamidreza; Vatandoost Hossein

来源：Journal of Engineering Mechanics, 2018, 144(9): 04018086.

DOI：10.1061/(ASCE)EM.1943-7889.0001515

• Nonlocal elasticity
• Annular graphene sheet
• Natural frequency
• First-order shear deformation theory
• Perturbation technique
• Engineering mechanics
• Dynamic analysis
• Nanostructure
• Mathematical models

This paper investigates the axisymmetric free vibrations of annular single-layered graphene sheets with different boundary conditions using nonlocal elasticity theory. The analysis procedure is based on the first-order shear deformation theory and small deflections assumption to derive the equations of motion which are a system of partial differential equations with variable coefficients. In order to determine the transverse natural frequencies as well as the radial natural frequencies analytically, the perturbation technique is applied to solve these equations. The transverse natural frequencies are calculated using classical plate theory. The results of both theories are compared with those obtained from the literature. A parametric study is performed and the effects of nonlocal parameter, geometry, and boundary conditions on the natural frequencies are investigated.

• 出版日期2018-9