Dynamics and phase-based vibration suppression of rotating flexible shaft with unstressed initial deformation under several parametric excitations

Abstract

A rotating flexible cantilever shaft is modeled with unstressed initial deformation under several parametric excitations, including fluctuant speed, axial force, torque and nonlinear radial follower force. Its dynamics is calculated via an improved Hill's method which is suitable for harmonic processing. An iteration method for solving the steady-state response of the nonlinear system's dynamics is proposed, and the stability is determined by the perturbation of the steady-state response. Considering the effects of a single excitation and different excitations’ coupling, two criteria for evaluating the system's dynamics are investigated by numerical simulation. One is the eccentric degree of the shaft's rotating deformation, and the other is the stability of the shaft system. The excitations’ coupling effect provides a novel method, called the phase-based vibration suppression method in this paper, to suppress the rotating deformation of a shaft with fluctuant speed or radial follower force by applying an extra fluctuant axial force or torque. Meanwhile, this systematic method to solve the steady-state dynamics of the shaft is universal for practical engineering.