Free vibration of new model of FG beams using state space approach

This work aims to study the natural frequencies of functionally graded beams by applying the higher-order shear deformation theory (HDT). The study focuses on the variation of mechanical properties across the beam's thickness. A new model of FGM beams is proposed, in which the material properties are governed by a novel power-law distribution of the volume fraction, varying from the exterior to the interior of the beam. By applying Hamilton's principle, the governing equations are derived using the state-space method. The accuracy of this method is demonstrated for the classical beam model, and the obtained results are validated through comparisons with previous studies. A comprehensive analysis is carried out to evaluate the impact of key parameters, such as the power-law index and the slenderness ratio, on the natural frequencies of functionally graded beams under various boundary conditions.