Abstract

Wave propagation along acoustic black hole waveguides (ABH) consisting of arrays of functionally graded perforated rings (FGPR) is investigated by developing their linearized electro-acoustic analog models. These models simulate the interactions between the different components of the ABH/FGPR as influenced by the design parameters of the perforated rings and coupled acoustic cavities. The developed electric analogs consist of arrays of resistors simulating the flow resistance through the perforations, inductances to quantify the inertia of the gas moving inside these perforations, and capacitances to describe the storage behavior of the cavities between neighboring rings. The dynamic interactions between these electric components are described by a state-space model in terms of the incoming and outgoing flow velocities as well as the pressures before and after each FGPR. In this manner, it is possible to determine the spatial distributions of the flow velocities and pressures along the ABH which are necessary to demonstrate the effectiveness of the proposed ABH/FGPR in generating the ABH effect by monotonically decelerating the flow along the waveguide and bringing it to a complete stop. The predictions of the developed electro-acoustic analog models are validated against the predictions of the classical “Transfer Matrix Method (TMM)” and experimental results established by Petrover and Baz (2025). Furthermore, these predictions are also validated against the predictions of a developed MATLAB SimScape Model of the electro-acoustic analogs. The comparisons between the predicted and measured results show close agreements and validate the accuracy of the developed electro-acoustic analog models.

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