Thermal vibration analysis and material optimization of three‐phase composite plate integrated with magneto–electro–elastic face sheets

Abstract In this study, the vibrational characteristics of a sandwich plate on an elastic foundation are examined under the combined effects of evenly applied external pressure, an electric field, a magnetic field, and uniform temperature rise. The structural configuration of the sandwich plate comprises five layers: a porous polymer core, a pair of intermediate layers composed of three‐phase composite (TPC) materials, and two exterior layers fabricated from magneto–electro–elastic (MEE) substances. Analytical formulations are employed to establish the overall properties of the TPC, which exhibit a nonlinear dependence on the volume fractions of the constituent materials and account for the interactions among them. The electric and magnetic fields are modeled as a superposition of sine–cosine functions together with linear components, in accordance with Maxwell's equations. Employing Reddy's higher–order shear deformation theory (HSDT), we formulate a closed–form model that incorporates von Kármán geometric nonlinearity together with initial imperfection effects, and elastic foundation effects represented through the Pasternak formulation. The vibration characteristics of the plate, including natural frequencies and the time–deflection response, are determined; the analysis employs the Galerkin scheme in combination with the fourth–order Runge–Kutta algorithm. Furthermore, the Bees Algorithm (BA) is applied to optimize and identify the maximum natural frequency with respect to six geometric and material parameters of the sandwich plate. Numerical results are presented through figures and tables to evaluate the influence of various parameters, including the elastic foundation coefficient, electric field coefficient, magnetic field coefficient, temperature increment, porosity coefficient, volume fractions of fibers and particles, and geometric parameters concerning the vibrational response of the three‐phase composite sandwich plate (TPCSP) with integrated MEE face sheets. Results derived from this study are contrasted with earlier publications to confirm their accuracy and reliability.