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.

In this paper, thermally-excited, lateral free vibration analysis of a small-sized Euler-Bernoulli beam is studied based on the nonlocal theory. Nonlocal effect is exerted into analysis utilizing differential constitutive model of Eringen. This model is suitable for design of sensors and actuators in dimensions of micron and submicron. Sudden temperature rise conducted through the thickness direction of the beam causes thermal stresses and makes thermo-mechanical properties to vary. This temperature field is supposed to be constant in the lateral direction. Temperatures of the top and bottom surfaces of the system are considered to be equal to each other. Governing equation of motion is derived using Hamilton’s principle. Numerical analysis of the system is performed by Galerkin’s approach. For verification of the present results, comparison between the obtained results and those of benchmark is reported. Numerical results demonstrate that dynamic behavior of small-sized system is been effected by temperature shift, nonlocal parameter, and slenderness ratio. As a result, taking the mentioned parameters into account leads to better and more reliable design in miniaturized-based industries.

In this paper, transverse vibration analysis of rotating micro-beam is investigated based on the modified couple stress theory. The simply-supported micro-beam is modeled utilizing Euler-Bernoulli and Timoshenko beam theories. The system is rotating around a fixed axis perpendicular to the axial direction of the beam. For the first time, displacement filed is introduced as a coupled field to the translational field. In other words, the mentioned rotational displacement field is expressed as a proportional function of translational displacement field using first (axial), second (lateral), and third (angular or rotational) velocity factors. Utilizing Hamilton’s approach as a variational method, dynamic-vibration equations of motion of the proposed model are derived. Galerkin’s method is adopted to solve the equation corresponding to the Euler–Bernoulli and Timoshenko beams. For the case considering shear deformation effects, Navier method is chosen. For evaluation of current results and models, they are compared with those available at the benchmark. In this paper; effects of slenderness ratio, axial, lateral, and angular velocity factors, and rotations of the beam on the frequency are reported. Based on the results presented, mentioned factors should be counted in the analysis and design of such rotating micro-systems.