Static and dynamic response of sector-shaped graphene sheets

ABSTRACT

Nonlocal elasticity theory is presented for the free vibration and bending analysis of nano-scaled graphene sheets having a sector shape. An eight-node curvilinear domain is used for transformation of the governing equation of motion of sector graphene from physical region to computational region in conjunction with the Kirchhoff plate theory. The discrete singular convolution method is employed for numerical solutions of resulting nonlocal governing differential equations and related boundary conditions. Then, the effects of nonlocal parameters, mode numbers, sector angles, and radius ratios on the static and vibration results of nano-scaled sector-shaped graphene sheets are discussed.

Keywords:

• Graphene sheet
• nonlocal elasticity
• sector shape
• discrete singular convolution
• vibration
• bending

Funding

The authors gratefully acknowledge partial financial support of the Scientific and Technological Research Council of Turkey (Tübitak/112M879).