Dynamic characteristics of cracked simply supported bidirectional functionally graded Rayleigh beam

This paper investigates the dynamic behavior of cracked Rayleigh beams constructed from bidirectional functionally graded (BDFG) materials under simple boundary conditions. A torsional massless spring is employed to model the beam's open crack type. The vibration equations are obtained using Hamilton's principle. The graded beam material properties are varied throughout the thickness based on the power-law distribution and in the longitudinal direction using the exponential material distribution. To solve the dynamic equations, Galerkin's approach is employed. The paper evaluates the impacts of the axial index, gradient property index, beam modulus ratio, and crack parameters on the natural frequencies of the FG beam. The results indicate that the dimensionless natural frequencies of intact graded beams decrease with increased gradient index k. In contrast, they increase with a rise in the modulus ratio. Additionally, the results demonstrate that an increase in the crack depth ratio decreases dimensionless natural frequencies.