Vibration analysis of micro-scaled sector shaped graphene surrounded by an elastic matrix

Free vibration analysis of micro-scaled annular sector and sector shaped graphene located on an elastic matrix are studied via nonlocal elasticity theory. An eight-node curvilinear element is used for transformation of the governing equation of motion of annular sector graphene from physical region to computational region in conjunctions with the thin plate theory. Elastic matrix is modeled via two-parameters which are Winkler–Pasternak elastic foundations. The discrete singular convolution (DSC) method is employed for numerical solution of resulting nonlocal governing differential equations and related boundary conditions. Then, the effects of nonlocal parameter, mode numbers, sector angles and foundation parameters on the frequency response of micron-scaled annular sector and sector graphene are discussed.