This study is concerned with the hydroelastic vibrations of sandwich micro-plates with functionally graded (FG) face sheets and metal core, interacting with sloshing liquid. For the purpose of the study, modified couple stress theory with variable length-scale parameter is applied to catch the small-scale effects of the structure. The mechanical properties of FG sandwich micro-plate and length scale parameter are supposed to be variable through the thickness of the structure. The displacement field is formulated based on fifth-order shear deformation theory which considers transverse shear stresses and rotary inertias. The liquid is assumed to be ideal, and the continuity equation is utilized to obtain liquid velocity potential associated with bulging and sloshing modes. After deriving kinetic and potential energies related to the micro-plate and liquid, Rayleigh-Ritz approach is applied to obtain vibrational characteristics of the system. Some comparison studies are made to confirm the reliability and efficacy of the present work. Finally, in the discussion section, wet frequencies of the sandwich micro-plate are analyzed in graphs and tables for various parameters.
