A new iterative method for free vibration analysis of a FG Timoshenko beam

In this study, the free vibration behavior of functionally graded Timoshenko beams is analyzed. The equations of motion are derived using Hamilton’s principle, resulting in fourth-order differential equations. By solving these equations, displacement and rotation functions are obtained. Applying appropriate boundary conditions yields a system of four linear equations, which constitute the coefficient matrix for various support scenarios. The fundamental frequencies are determined by identifying the points where the determinant of this matrix equals zero. To efficiently locate these points, a novel iterative method is proposed. The results are validated through comparisons with existing studies in the literature and are illustrated with comprehensive tables and figures.