Analysis the free vibration of functionally graded material plate by using new displacement function

• It was used a novel displacement function to perform the free vibration analysis of functionally graded materials plates (FGM). • The displacement field at the mid-surface of FG plate is expanded in a trigonometric series in the thickness direction. • The governing equations are derived using Hamilton's principle, and then the Navier technique by MATLAB 2021. • To verify accuracy, the obtained results from this method are compared with the literature and ANSYS results. • The natural frequency of simply supported FG plate is calculated under different length-to-thickness ratio and various power law indexes, while the proposed method offers a closed results to other methods from literature. This work introduces a new displacement function for the free vibration analysis of functionally graded material (FGM) plates, combining analytical modeling and finite element analysis using ANSYS. The displacement field at the mid-surface is represented by a trigonometric series in the thickness direction. Governing equations are derived via Hamilton's principle, solved analytically using the Navier technique in MATLAB 2021, and validated through ANSYS simulations. Results show excellent agreement across various power-law indices, thickness ratios, and aspect ratios to verify data within the literature. The findings reveal a reduction in natural and dimensionless frequencies with increasing length-to-thickness ratios and power-law indices. However, when the modulus of the metallic material is greater than that of the ceramic material, the non-dimensional frequencies decrease as the power-law index increases. underscoring the precision and versatility of the proposed methodology for dynamic analyses of FG-plates.