(untitled) (Advances in Applied Mathematics and Mechanics, 2025)
This study investigates the dynamic response of functionally graded saturated porous (FGSP) nanoplates resting on the elastic foundation. The porosities are assumed to vary gradually through the thickness of the plate, following three different patterns: uniform, non-uniform symmetric, and non-uniform asymmetric distributions. Biot’s poroelasticity theory is employed to describe the stress-strain relation of functionally graded porous materials when in a liquid-saturated state. Additionally, the nanoscale effects of the structure are taken into account by incorporating Eringen’s nonlocal elasticity theory. The equations of motion are formulated by applying Hamilton’s principle, utilizing a quasi-three-dimensional higher-order shear deformation (quasi-3D HSDT) theory. This theory guarantees that the top and bottom surfaces of the nanoplate experience conditions free of transverse shear stress. The obtained results reveal that the free vibration and transient response of the FGSP nanoplate is significantly influenced by various factors, including the porosity coefficient and distribution patterns, geometrical parameters, elastic foundation stiffness, Skempton coefficient, and nonlocal parameters. The theoretical development as well as numerical solutions presented herein offer valuable insights and serve as a reference for nonlocal theories of FGSP nanoplates.