Free vibration behavior in functionally graded material plates with dual efficient quadrilateral finite elements

Functionally graded materials represent advanced composites with typically two materials that exhibit gradual variations in their mechanical properties throughout the structure's thickness in general, as determined by a presumed mathematical model. The current investigation focuses on analyzing free vibrations of functionally graded material plate structures with two efficient isoparametric quadrilateral finite elements (Lagrange and Serendipity) together for the first time and different material combinations based on first-order shear deformation theory. The analysis was carried out on relatively thin as well as medium thick functionally graded plates with varying power law indices and at varied boundary conditions. The framework equation was formed with Hamilton's principle, and solutions were done with finite element method, considering a shear correction factor for the behavioral study of varying material properties. The findings align well with the information presented in prior literature. After validating the present model, parametric analysis was conveyed to show the impact of length-to-thickness ratio, aspect ratio, volume fractions, and skew angles for two novel materials on the fundamental frequencies and mode shapes. The results thus obtained with the two quadrilateral elements have a significant effect on the changes in these parameters. Also, the natural frequencies of different functionally graded plates, including two novel materials, were compared and discussed.