Abstract
In this paper, higher order frequency response functions, based on the Volterra series, are employed to characterise the input-output behaviour of the non-linear viscous Burgers’ equation subject to sinusoidal excitation. First, a formal Volterra series representation for each spatial location is derived for the solution of Burgers’ equation with a boundary condition as the input to the system. Then a systematic method is presented to obtain the higher order frequency kernels of the Volterra series at each spatial location by solving a series of ordinary differential equations. It is shown that the convergence region of the individual harmonics with respect to the magnitude of the input excitation can be estimated by using these higher order kernels. The frequency characteristics of Burgers’ equation is investigated and compared with numerical simulation.
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