A Volterra series approximation to the coherence of the Duffing oscillator

Following previous work on computing approximate frequency response functions for the Duffing oscillator under white Gaussian excitation, an approximation is obtained here for the coherence function. A Padé approximation of order (1,1) is made for the asymmetric Duffing oscillator (i.e. with non-zero quadratic term), and an approximation of order (2,2) is made for the symmetric (no quadratic term) oscillator. The analytical results are shown to give excellent qualitative agreement with numerical simulation. However, in quantitative terms, the approximations underpredict the coherence distortion as is consistent with the low-order truncations of the Volterra series.