Nonlinear free vibrations analysis of rotating shaft based on the Timoshenko beam theory with stretching nonlinearity

• Published in: Advances in mechanical engineering 2017-01, Vol.9 (1)
• Main Authors: Mirtalaie, Seyed Hasan, Hajabasi, Mohammad Ali
• Format: Article
• Language: English
• Subjects: Authorship; Boundary conditions; Finite element analysis; Gas turbine engines; Journal bearings; Researchers; Shear strain; Studies; Vibration analysis
• ISSN: 1687-8132; 1687-8140
• DOI: 10.1177/1687814016688589

The nonlinear axial–lateral free vibration behavior of the rotor is investigated by a new sight to the Timoshenko beam theory. In the modeling of the system based on this new nonlinear dynamic model in which the nonlinearities are originated from the stretching of beam centerline, the effects of rotary inertia, gyroscopic forces, and shear deformations are taken into account but the torsional deformation is neglected. According to this new methodology in which the curved geometry of the beam is represented by the Euler angles and the shear deformations, a nonlinear system of coupled variable-coefficient differential equations is derived which is solved by the method of multiple scales in order to determine the nonlinear natural frequencies. The accuracy of the solution method is inspected by comparing the numerical results with the results of two other beam theories and also by the comparison of the free vibration response obtained by the perturbation technique with the numerical integration of the governing equations. The effect of various parameters such as the rotational speed, slenderness ratio, and shear-to-bending stiffness ratio on the free vibrations of the system is inspected. The study demonstrates the nonlinear stretching effect on the free vibration behavior of the shear deformable spinning beam.