Effect of the porous structure on the hygrothermal vibration analysis of functional graded nanoplates using nonlocal high-order continuum plate model

Abstract This study delves into the thermomechanical vibration behavior of functionally graded porous nanoplates under extreme thermal temperature and humidity conditions. The equation of motion of the nanoplate was derived using advanced theories in elasticity and deformation. The nanoplate consists of metal (SUS304) on the bottom surface and ceramic (Ni 3 S 4 ) on the top surface, with the material distribution changing according to the power law across the plate thickness. The nanoplate was modeled with uniform and symmetric distributions of porosity reaching as high as 60%. Upon incorporating the thermal and moisture loads from the humid surroundings into the equations of motion derived from Hamilton's principle, the equations were solved using Navier's method and simplified to the eigenvalue equation. Analyzed within a broad framework are the thermomechanical vibration behavior of the nanoplate, temperature impact, humidity influence, porosity and its distribution, material grading parameter effects, and nonlocal integral elasticity effects. Observations indicate that variations in thermal temperature, humidity, and nonlocal parameters can lower the thermomechanical vibration frequency of the nanoplate, whereas porosity has the opposite effect. The effects mentioned are influenced by factors, such as the porosity ratio, porosity distribution, material ratios, and the size of the nonlocal parameter in the plate. The primary objective of this work is to uncover the nonlinear frequency response of nanoplates with high porosity in conditions characterized by high temperature and humidity.