Isogeometric vibration analysis of functionally graded nanoplates with the consideration of nonlocal and surface effects

Presented in this paper is a size-dependent analysis of the surface stress and nonlocal influences on the free vibration characteristics of rectangular and circular nanoplates. Nanoplates are assumed to be made of functionally graded materials (FGMs) with two distinct surface and bulk phases. The nonlocal and surface effects are captured by the Eringen and the Gurtin-Murdoch surface elasticity theories, respectively. The Mori-Tanaka distribution scheme is also used for obtaining material properties of nanoplate. In addition to the conventional procedure of deriving the formulation, a novel matrix-vector form of the governing differential equations of motion is presented. This form has the capability of being used directly in the finite element method or isogeometric analysis. To show the effects of surface parameters and small scale influences on the vibrational behavior of rectangular and circular FGM nanoplates with various boundary conditions, several case studies are presented.