Abstract：The axially translating cantilevered beams are widely used in engineering. The vibration of the beams will exert great effect on the safety and reliability of the system. Dynamic analysis of an axially translating functionally graded (FG) cantilevered beam is investigated. The equations of the system are derived by the Hamilton’s principle with the assumed mode method. And the coupled equations of motion are gotten. The properties of FG materials are functionally graded in the thickness direction according to the volume fraction power-law distribution. A tip mass is considered to be concentrated at the free end of the beam. The effects of the power-law exponent and tip mass on the vibration are discussed. Moreover, the movement characteristics of the FG beam during the extension mode and the retraction mode are analyzed. The conclusions of this paper give a basis for dynamic analysis and design of similar structures.
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