This paper presents an analytical investigation in the free vibration of a cracked Timoshenko beam made up of functionally graded materials (FGMs). A crack is modeled by a rotational spring and the perspective of wave method is adopted for the analysis. The method considers the nature of the propagation and reflection of the waves along the beam. Consequently, the propagation, transmission and reflection matrices for various discontinuities such as crack, boundary barrier or change in section, which is located on a beam are derived. By combining these matrices a global frequency matrix is formed. The obtained characteristic equation is solved analytically to achieve the natural frequencies.

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