Isogeometric nonlinear oscillations of nonlocal strain gradient PFGM micro/nano-plates via NURBS-based formulation

Abstract

The present investigation deals with the size-dependent analysis of the geometrically nonlinear vibration response of micro/nano-plates with and without a central cutout made of a porous functionally graded material (PFGM) in the presence of nonlocality and strain gradient size dependencies. In accordance with this purpose, a modified porosity-dependent power-law function is put to use to estimate the effective mechanical properties of PFGM micro/nano-plates with various porosity distribution patterns. To solve the constructed nonlinear nonlocal strain gradient problem, the non-uniform rational B-spline (NURBS)-based isogeometric analysis is utilized as an efficient discretization technique having the capability to satisfy C-1 continuity. It is seen that for specific values of the material property gradient index, porosity index and the plate deflection, the enhancement in the nonlinear frequency due to the strain gradient size effect is more than the reduction caused by the nonlocality. Furthermore, it is found that there is a specific value of the length to thickness ratio, corresponding to which the nonlocal strain gradient frequency ratio becomes minimum. This minimum value enhances by increasing the value of the porosity index of PFGM micro/nano-plates. Also, by increasing the value of the material property gradient index, the minimum point of the nonlocal strain gradient frequency ratio shifts to a higher ratio of the length to width ratio.