Vibration analysis of rotating thermally-stressed gyroscope, based on modified coupled displacement field method

Free lateral vibration analysis of gyroscope model is studied in this paper. This gyroscope is modeled as a rotating simply-supported beam which is under an initial thermal stress. Thermo-mechanical properties of the beam are mutable with temperature. For the first time beam is supposed to rotate around a fixed axis in which rotational displacement field is expressed as a liner function in terms of combination of axial and lateral displacements. Dynamic-vibration equations of the proposed model are derived based on the Hamilton's principle. Due to the symmetry of the system, Navier approach is adopted as solution approach. For evaluation, current results are compared with the results available at the technical literature showing high level of accuracy. New results emerged from of this paper imply effects of rotation of the beam and thermal stresses simultaneously upon the dynamic response of beams: different values of lateral velocity factor strongly affect the frequencies of the system; however, axial velocity factor does not play any role. In short, rotation of the beam accompanied by thermal stresses are affecting the dynamic behavior of the beam-type gyroscope remarkably. Consideration of thermal stresses and rotation rates are the most vital factors in the design of a gyroscope.