Dynamic instability analysis of piezoelectric fluid-infiltrated porous metal foam nanosheet considering surface and flexoelectricity effects in hygro-thermal environment

The main goal of this work is to present the free oscillation, static and dynamic buckling of piezoelectric fluid-infiltrated porous metal foam (FPMF) nanosheet lying on Pasternak medium in the hygro-temperature environment with consideration of the surface and flexoelectricity effects. Employing the nonlocal strain gradient hypothesis in conjunction with refined higher-order shear deformation plate theory (HSDT), the motion equations are derived via Hamilton’s variational principle. The novelty of this study is that the two nonlocal and length-scale coefficients are variable along with thickness, like other material characteristics. Galerkin approach as well as Bolotin’s method are utilized to obtain the dynamic instability region of the piezoelectric FPMF nanosheet. The accuracy of the proposed method is verified through reliable publications. The outcome of this study highlights the significant effects of the nonlocal and length-scale parameters on the vibration and buckling behaviors of piezoelectric FPMF nanosheets. Because it integrates the ideas of nonlocal strain gradient, flexoelectricity, and surface effects for piezoelectric FPMF nanosheets, the current work is broadly applicable. This work clarifies the understanding of the fundamental physics of electromechanical interaction at the piezoelectric FPMF nanosheet, a subject that has not been studied much yet. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.