Resonant response functions for nonlinear oscillators with polynomial type nonlinearities

In this paper we consider the steady-state response of forced, damped, weakly nonlinear oscillators with polynomial type nonlinearities. In particular we define general expressions that can be used to compute resonant response functions which define the steady-state constant amplitude oscillatory response at the primary resonance and the associated harmonics. The resonant response functions are derived using a normal form transformation which is carried out directly on the second-order nonlinear oscillator. The example of a forced van der Pol oscillator with an additional cubic stiffness nonlinearity is used to demonstrate how the general analysis can be applied.