Free and Forced Vibration of Sandwich FGM Porous Variable Thickness Nanoplates Integrated with Magneto-Electro-Elastic Layers Via Nonlocal Strain Gradient Theory

In the present study, free and forced vibration analysis of sandwich smart magneto-electro-elastic (MEE) nanoplates with functionally graded material porous (FGMP) of linearly or parabolically varying thickness core layer under initial external electric and magnetic potentials is studied using the first-order shear deformation theory (FSDT) and nonlocal strain gradient theory (NSGT). NSGT is perfected with softening and hardening material effects, which can significantly improve the precision of results. Three states of porosity distribution patterns, i.e., even, uneven, and logarithmic-uneven porosity distributions are considered for the FGMP core layer, which are supposed to vary along the in-plane and thickness directions. The related governing equations are obtained in the time domain by applying Hamilton's principle. The established solution is examined in terms of its precision via a comparison with other available data. Studies of the parameters show the effects of the unidirectional and bidirectional taper constants, initial electric and magnetic potentials, porosity distributions, FG index, nonlocal and strain gradient characteristics on the free and forced vibration.