Fourier expansion solution for a switched shunt control applied to a duct

In the present work, a semi analytic approach aimed at estimating the effects on reduction of the pressure sound level by synchronised switched shunt logic is described. The displacement field within a 1D longitudinal air column through a Fourier series expansion has been formalised by assigning a sinusoidal perturbation and fluid-structure interface condition on the left and right boundaries, respectively. To simulate the no control operative condition, the solution has been computed for the entire time domain, keeping invariant all circuitry properties; then for the switch working modality, the solution has been computed by splitting the entire time domain into partitions; for any partition, specific circuitry properties (e.g. piezo voltage, electrical field...) have been selected. Based on the displacement information, the related sound pressure level has been compared for no controlled and controlled operative conditions, with and without signal amplification.