Vibration behavior of stiffened functionally graded porous sandwich plates with a magneto-electro-elastic face resting on an elastic foundation under hygrothermal, electrical, and magnetic fields

This article investigates the free vibration behavior of a stiffened sandwich plate subjected to combined hygrothermal, electrical, and magnetic fields and resting on a Pasternak elastic foundation. The porous functionally graded magneto-electro-elastic sandwich plates (PoFG-MEES) consists of three layers: a top layer made of PoFGMEE (porous magneto-electro-elastic functionally graded materials), a core of functionally graded material with porosity (PoFGM), and a bottom layer, which incorporates stiffeners made from the same perfect functionally graded material. The through-thickness variation of material properties is modeled using a modified power-law function with two porosity distribution patterns, while the electric potential and magnetic field in the PoFGMEE layer follow combined cosine–linear profiles. The proposed model employs a higher-order shear deformation theory (HSDT-4), the pb2-Ritz method, and Lekhnitskii’s smeared stiffener technique to account for material gradation, porosity distribution, and stiffener reinforcement under various boundary conditions. Numerical results, validated against existing literature, reveal that porosity distribution, material volume fractions, foundation stiffness, external fields, and stiffener configuration significantly influence the natural frequencies. Specifically, a Pasternak foundation and optimized stiffener arrangements enhance structural stiffness, while electric and magnetic fields can either increase or decrease frequencies depending on their polarity. The findings provide valuable insights for designing smart structures and stiffened sandwich plates operating under coupled hygrothermal, electrical, and magnetic fields.