This paper presents modelling and dynamic analysis of an on-board rotor with base excitation. A flexible shaft and rigid disc model is considered for idealizing a turbocharger rotor. The nonlinear hydrodynamic journal bearing forces are computed and the discretized equations of motion using finite element method are solved with time integration scheme. The disc unbalance forces are also accounted. The instability regions are identified by inducing varying sinusoidal support excitations. The work gives insights in design of the automobile engine turbocharger rotor mounted on hydrodynamic journal bearings supported with viscoelastic springs. © 2016 The Authors.