Analytical Description of the Frequency Response Function of the Generalized Higher Order Duffing Oscillator Model

Existing algorithms for computing the
n
th-order frequency response functions of the Duffing oscillator have helped promote frequency domain analysis of nonlinear systems but still have a number of practical difficulties. A very efficient algorithm to enable the
n
th-order symmetric generalized frequency response functions (GFRFs) to be written down directly in terms of the coefficients of the generalized higher order Duffing oscillator model is developed in this paper. The analytical expression derived in this paper shows that the key procedure in the determination of the higher order GFRFs is the computation of the Stirling set of the second kind. This enables the structure of the higher order GFRFs to be seen more clearly.