Nonlinear vibration analysis of a flexible rotor shaft with a longitudinally dispositioned unbalanced rigid disc

Abstract

This study aims to investigate the nonlinear dynamics of a rotor system of a flexible rotor shaft carrying an unbalanced rigid disc. For this purpose, the dynamics of three different rotor systems are analysed in this study. First, the dynamics of a system of an unbalanced flexible rotor shaft is examined. Second, vibration analysis and a parametric study are carried out on a system of an unbalanced rigid disc located at the mid-point of a rotor flexible shaft. The third system is composed of a flexible rotor shaft carrying a longitudinally dispositioned unbalanced rigid disc. The flexible shaft is modelled using the Euler-Bernoulli beam theory. Geometrical and inertial nonlinearities of the flexible shaft are considered in the mathematical modelling of the structure. The extended Hamilton principle is utilized to derive the nonlinear equations of motion of the described system. The obtained nonlinear governing equations are discretized using the assumed mode method and applying the Galerkin method to the equations of motion. In this study, a two-mode reduced order model is used to investigate the nonlinear dynamics of the rotor systems. The resultant discrete nonlinear equations of motion are solved using direct numerical integration. The results of the first case study are used to verify the accuracy of the theory and methods used in this study. Then, the results of the parametric study are presented. The effects of various parameters of the system are investigated on the dynamic behaviour of the structure. Finally, the chaotic response of the third case is investigated using the numerical simulation of the dynamics of the system.