Free vibration of bi-dimensional functionally graded simply supported beams

This paper investigates the free vibration of bi-dimensional functionally graded simply supported beams by using the continuous element method. The material properties are considered to vary exponentially along the beam thickness and length. The characteristic frequency equations of simply supported beams are derived by transfer matrix method. Validation targets are other analytical methods. The effects of the gradient indexes and the beam slenderness ratio on the natural frequencies of bi-dimensional functionally graded beams are studied.