Analysis of Nonlinear System Response to an Impulse Excitation

The paper investigates the use of a Volterra series-based approach to explain the impulse response behaviour of nonlinear systems. Analytical expressions are derived using a frequency-domain based approach with the contour integration being conducted using the calculus of residues. The complexity of the process and the resulting expressions increases dramatically as the order of the response component increases and, for this reason, the work only considers the linear component of the impulse response and the first two nonlinear Volterra series components. The effect of including these components is then investigated by comparing the impulse responses from the Volterra expressions to the impulse response of a simulated single degree of freedom Duffing oscillator system. It is found that these components are capable of drastically decreasing the error when compared with the linear impulse response but, at higher forcing levels, the Volterra approach can suffer from convergence problems which may result in worse predictions than the linear response.