Equivalent oscillator model for the nonlinear vibration of a porter governor

Abstract

The nonlinear free vibration of a porter governor was investigated using an equivalent oscillator model (EOM). The equivalent oscillator model, whose exact periodic solution was derived in terms of the complete elliptic integral of the second kind, was formulated based on quasi-static equilibrium conditions. The derived equivalent oscillator constants for the porter governor were found to be dependent on the maximum potential energy and restoring force of the governor. Simulations of the derived approximate solution for the frequency-amplitude response of the porter governor were found to be in good agreement with corresponding numerical solutions. Investigations showed that the frequency of oscillation of the porter governor decreases with increase in the ball-sleeve mass ratio, rotational speed of the governor and/or arm length.

Keywords

• Porter governors
• Equivalent oscillator model
• Elliptic integral
• Non-natural oscillators
• Quasi-static equilibrium