Approximate Analytical Solutions to Nonlinear Oscillations of Horizontally Supported Jeffcott Rotor

Abstract

The present paper focuses on nonlinear oscillations of a horizontally supported Jeffcott rotor. An approximate solution to the system of governing equations having quadratic and cubic nonlinearities is obtained in two cases of practical interest: simultaneous and internal resonance. The Optimal Auxiliary Functions Method is employed in this study, and each governing differential equation is reduced to two linear differential equations using the so-called auxiliary functions involving a moderate number of convergence-control parameters. Explicit analytical solutions are obtained for the first time in the literature for the considered practical cases. Numerical validations proved the high accuracy of the proposed analytical solutions, which may be used further in the study of stability and in the design process of some highly performant devices.

Keywords

• nonlinear oscillations
• rotor dynamics
• asymmetric nonlinearity
• simultaneous and internal resonance
• optimal auxiliary functions method