Vibration analysis of FG sandwich plates using inverse trigonometric shear deformation theory in finite ‐ element framework

This paper presents a finite element framework for vibration analysis of functionally graded sandwich plates (FGSPs) using inverse trigonometric shear deformation theory (ITSDT). Two configurations are examined: plates with an isotropic core and FG face sheets, and plates with an FG core and isotropic face sheets. The study evaluates the free vibration behavior including shear deformation and rotary inertia effects. ITSDT employs an inverse trigonometric function to represent shear deformation, improving accuracy without requiring shear correction factors. The material characteristics of the FG layers exhibit a continuous variation across the thickness according to power-law distribution. A finite element framework is formulated, where the governing equations are obtained using Hamilton’s principle and subsequently solved. The proposed approach is capable of handling various edge constraints, such as simply supported, clamped, and mixed boundary conditions, thereby addressing the restrictions of analytical solutions that are generally limited to simplified configurations. Validation against existing results confirms accuracy and applicability. A comprehensive parametric study investigates the influence of material gradation, thickness configuration, span-to-thickness ratio, and boundary conditions. Results indicate that FG distribution, core-to-face thickness ratio, and boundary constraints significantly affect vibrational characteristics, demonstrating the robustness and applicability of the proposed framework for complex engineering structures.