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In this article, the nonlocal strain gradient theory (NSGT) has been utilized to reveal the dynamic investigation of bi-directional (2D) functionally graded (FG) porous nanoplates resting on Winkler and Pasternak elastic foundations. The governing formulations are derived via Hamilton’s principle, first-order shear deformation theory (FSDT), von-Karman geometrical nonlinearity and the principal of mixtures. It is presumed that the materials graded in two directions and two different distributions of porosities including even and uneven patterns through the thickness of the FG nano-scale plate. The nonlinear equations are solved via the kinetic dynamic relaxation (KDR) numerical procedure and the Newmark integration as well as finite-difference discretization approach. In order to validate the present numeric outcomes, some comparison studies have been conducted with available papers. The parametric study of this paper reveals the roles of different effective factors such as porosity coefficients, nonlocal and strain gradient parameters, diverse boundary conditions, gradient indexes and elastic foundations on the dimensionless deflection. It can be inferred that nonlocal parameter and specially strain gradient coefficient affect the variations of deflection. Eventually, it can be comprehended that elastic foundation in even porosity distribution affects the deflection more remarkably than uneven porosity.

A nonlocal strain gradient model for nonlinear dynamic behavior of bi-directional functionally graded porous nanoplates on elastic foundations