Small scale effects on the vibration response of functionally graded nanoplates using a nonlocal continuum model

Abstract

In the present work, a refined trigonometric higher-order shear deformation theory has been presented in conjunction with nonlocal theory for the vibrational response of functionally graded (FG) porous nanoplate. The displacement field is chosen based on assumptions that the out-of-the-plane displacement consists of bending and shear components whereas the transverse shear-strain has nonlinear variation along the thickness direction. The number of unknown variables are four, as against five or more in other renowned shear deformation theories. The governing equations have been derived using Hamilton s principle. A generalized porosity model has also been developed to accommodate both even and uneven types of distribution of porosity in the FG nanoplates. The closed-form solution of simply-supported FG porous nanoplates is obtained and the results are compared with the available reported results. In finite element solution, a C0 continuous isoparametric quadrilateral element has been used with various conventional and unconventional boundary conditions. The effects of various parameters like small-scale effect, aspect ratio, volume fraction index, porosity volume fraction, and thickness ratio have been investigated.