Premium
Forced vibrations of nonlinear symmetrical and asymmetrical rotating shafts mounted on a moving base
Author(s) -
Shahgholi Majid,
Payganeh Gholamhassan
Publication year - 2019
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201700097
Subject(s) - asymmetry , nonlinear system , vibration , physics , perturbation (astronomy) , amplitude , principal axis theorem , equations of motion , classical mechanics , inertia , multiple scale analysis , excitation , boundary value problem , mechanics , mathematical analysis , mathematics , geometry , optics , acoustics , quantum mechanics
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.