Forced vibrations of nonlinear symmetrical and asymmetrical rotating shafts mounted on a moving base

Abstract

This paper deals with the combinational resonances of symmetrical and asymmetrical rotating shafts with base motions. The nonlinearities are owing to the large amplitude of the hinged‐ hinged the shaft. Generally, the asymmetrical shaft has unequal principal mass moments of inertia and flexural stiffnesses. The system is exposed to three sources of excitation as a result of the asymmetry of the shaft, dynamic imbalances, and base excitations. Using the variational approach the nonlinear governing equations of motion and related boundary conditions are derived in the complex form. These equations of motion are analyzed by the use of the perturbation method. It is shown that three combinational resonances occur in the system. In the two cases of combinational resonances the asymmetry of shaft has no effect on the steady‐state responses. However, in one case of the combinational resonances, the asymmetry of the shaft has a significant effect. Also, in each case, the steady‐state solutions and their stability are investigated. The effect of various parameters such as damping coefficient, eccentricities, and asymmetry of the shaft on the periodic solutions, the stability of the solutions and bifurcations are probed. Additionally, the analytical results are verified by the numerical simulations that are obtained a good agreement between these results.

Combination resonances of spinning composite shafts considering geometric nonlinearity

“…One-mode discretization is performed in this section. The following expression is assumed for spatial form of the response [20,22]:…”

“…Their results showed that the parametric excitation could be used to control the vibration. Shahgholi and Payganeh [22] studied the combination resonances of an asymmetrical metallic spinning shaft having moving base using the method of multiple scales. There were three excitations in their research which were due to imbalances, asymmetry, and base movement.…”

Dynamics of on-board rotors on finite-length journal bearings subject to multi-axial and multi-frequency excitations: numerical and experimental investigations

“…Other contributions were devoted to onboard rotors with geometric nonlinearities caused by large shaft displacements. This was the case of Phadatare et al [18] with their highly flexible shaft mounted on a base subject to sinusoidal vertical translations and of Shahgholi et al [19] with their asymmetric shaft whose support was subject to sinusoidal transverse rotations. In both these works, the shaft dynamics was restricted to the first mode of the linear system to facilitate the application of perturbation methods.…”

Dynamic analysis of nonlinear rotating composite shafts excited by non‐ideal energy source

“…To be more precise, in isotropic case: Hosseini and coworkers studied different aspects of nonlinear rotating shafts . Shahgholi and Payganeh analyzed the symmetrical and asymmetrical rotating shafts mounted on a moving base.…”