Effect of Orthotropic Variable Foundations and Unconventional Support Conditions on Nonlinear Hygrothermoelectric Vibration of Porous Multidirectional Piezoelectric Functionally Graded Nonuniform Plate

ABSTRACT This article investigates the nonlinear vibration behavior of porous multidirectional piezoelectric functionally graded nonuniform (PFGN) plates resting on orthotropic variable elastic foundations and subjected to hygrothermal loading. The sigmoidal law is employed to define the multidirectional gradation properties, incorporating porosity along both the axial and thickness directions. The governing equations for the porous multidirectional PFGN plate are derived using the modified first‐order shear deformation theory (FSDT) with nonlinear von Kármán strain and Hamilton's principle. A higher‐order finite element (FE) approach, combined with a modified Newton‐Raphson method, is utilized to solve the resulting equations. The study reveals that orthotropic variable elastic foundations significantly influence the vibration behavior of multidirectional PFGN porous plates compared to conventional elastic foundations under hygrothermal loading. Additionally, the effects of various parameters such as thickness ratio, tapered ratio, material exponent, boundary conditions, porosity distribution, electrical loading, temperature variation, and moisture change on the vibration behavior are comprehensively analyzed. The results of this study have direct applications in energy harvesting and structural health monitoring, offering a novel approach to designing and optimizing smart materials for engineering systems operating under hygrothermal and thermoelectrical conditions.