Vibration of Cracked Timoshenko Beam Made of Functionally Graded Material

Functionally Graded Material (FGM) is an advanced composite that finds increasing application in high-tech industries such as mechatronics, space technology, bio-materials etc. In the application of FGM, dynamics of structures such as beams, plates or shells made of the material is of a great importance. This report is devoted to develop general theory of vibration of cracked FGM beams based on the power law of material grading and Timoshenko beam theory. Crack is modeled by an equivalent spring of stiffness calculated from its depth. First, governing equations of motion of the beam are constructed in the frequency domain taking into account the actual position of beam neutral plane. This enables to obtain general solution of free vibration of the beam and condition for uncoupling of axial and flexural vibration modes. Using the solution natural frequencies and mode shapes of cracked FGM beam are examined in dependence upon material properties and crack parameters.