▎ 摘　　要

Effects of a single vacancy defect or a pin hole on free vibration behavior of a double layer graphene sheet are investigated. Using the nonlocal continuum theory as well as the Gurtin-Murdoch theory, the nonlocality and surface effects are considered in equations of motion. Both of in-phase and anti-phase vibration modes are analytically analyzed. Employing the translational addition theorem for cylindrical vector wave functions, the geometrical defect as a circular hole in arbitrary size and location is modeled. The van der Waals interaction between the upper and lower layers is included using the Lennard-Jones pair potential. The computational efficiency and accuracy of results are validated by literature. Effects of boundary conditions, geometrical properties, nonlocality and surface effect parameters on in-phase and anti-phase vibrational modes are investigated. Results reveal that the fundamental natural frequency of an annular double-layer graphene sheet with a free eccentric circular defect is less affected by the size and location of the defect. Moreover, the surface effect parameters have more significant effects on the in-phase vibration modes than the anti-phase ones. (C) 2015 Elsevier Ltd. All rights reserved.