The Galerkin-Vlasov approach based on the improved first-order shear deformation theory (i-FSDT) and nonlocal elasticity theory are proposed to investigate the free vibration response of variable-thickness fluid-infiltrated porous metal foam (FPMF) nanoplates with flexoelectricity effect resting on Pasternak elastic foundation in the hygro-thermal environment. The FPMF nanoplate thickness varies according to both the length and width directions. The novelty of the present work is to consider the influence of the nonlocal's spatial variation and flexoelectric coefficients on the free vibration behavior of the nanoplates. Based on Hamilton's principle, the governing equation of FPMF nanoplate is established. The accuracy of the proposed method is checked by comparing the obtained results with those of available work in the literature. The effects of the parameters such as the flexoelectric coefficient, nonlocal coefficient, porosity coefficient, Skempton factor, temperature and moisture, thickness variation, and various boundary conditions on the natural frequency of the nanoplate are examined.
Keywords: Analytical solution; Flexoelectricity; Free vibration; Nanoplates; Variable thickness.
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