Study of the Effect of Non-linear End Supports on the Unbalance Response of the Elastic Shaft

Non-linearities in modelling the dynamic behaviour of systems are often neglected for simplicity; however, accurate prediction of responses, especially in the cases of low tolerance on response, and the issue of stability justify the application of non-linear dynamic model of a system. This study focuses on the analytical prediction of the unbalanced response of a Jeffcott rotor with rolling element bearings at ends supported on viscoelastic supports, and the role of support damping on the non-linear dynamic behaviour, particularly the undesirable jump phenomenon of the rotor. Deformation-dependent stiffness of rolling element bearings makes the system of equations non-linear. A detailed study with non-dimensional parameters is attempted to find optimum damping for minimizing the response.