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In practical operations of mechanical structures, it is not difficult to meet some large components such as helicopter rotors, gas turbine blades of marine engines, and rotating railway bridges, where these elements can be seen as beam models rotating around one fixed axis. Therefore, mechanical explorations of these structures with and without the effect of temperature will guide the design, manufacture, and use of them in practice. This is the first paper that uses the shear deformation theory-type hyperbolic sine functions and the finite element method to analyze the free vibration response of rotating FGM beams with initial geometrical imperfections resting on elastic foundations considering the effect of temperature. The material properties are assumed to be varied in the thickness direction of the beam based on the power law function and temperature changes The proposed theory and mathematical model are verified by comparing the results with other exact solutions. The numerical investigations have taken into account some geometrical and material parameters to evaluate the effects on the vibration behavior of the structure such as the rotational speed, temperature, as well as initial geometrical imperfections. The drawn comments have numerous scientific and practical implications for rotating beam structures.

Free Vibration Investigations of Rotating FG Beams Resting on Elastic Foundation with Initial Geometrical Imperfection in Thermal Environments