Abstract
Free vibration of cracked multistep beam made of functionally graded material is studied on the basis of the Timoshenko beam theory and actual position of neutral plane of functionally graded beam. Crack model is adopted using a pair of translational and rotational springs of stiffness calculated from the same crack depth. An exact dynamic shape function is proposed and used to conduct a simplified transfer matrix for cracked uniform functionally graded beam element. Frequency equations of the cracked multistep beam established in the form of 3 × 3-dimensional determinant for different cases of boundary conditions are employed for analysis of natural frequencies in dependence on the crack position and depth, material properties and size of beam steps. It was shown that abrupt variation of beam thickness has significant effect on the sensitivity of natural frequencies to cracks. This is demonstrated by numerous results obtained for beam with three steps in different boundary condition cases.
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