Dynamic response analysis of functionally graded plates using analytical solution and the P-version of the finite element method

This study presents comprehensive analysis of the dynamic behavior of plates made from functionally graded materials (FGMs), emphasizing central deflection subject to various effects and boundary conditions using two different theories. A novel analytical solution is developed using the Classical Plate Theory in order to study the dynamic behavior of FGM plates. In parallel with this analytical approach, the p-version of the Finite Element Method is applied, incorporating the first order shear deformation theory and the mode superposition method to account for higher-order effects and achieve numerical precision. The study demonstrates an excellent agreement using both the analytical and numerical solutions. Through this combined approach, the dynamic behavior of FGM plates is comprehensively analyzed, revealing the significant effect of different parameters including the volume fraction exponent, material composition, length–width ratio, thickness ratio, damping coefficient, and boundary conditions. It is demonstrated that these parameters have a crucial influence on the dynamic response amplitude of plates, offering important insights for the design and optimization of FGM structures in practical uses.