Nonlinear regression-based method for determining the effective length of complex folded acoustic cavities for enhanced low-frequency sound absorption

Increasingly intricate folded cavity absorbers are being proposed to minimize the thickness of metamaterials. Nevertheless, there has been scant research on determining the effective length of complex folded cavities. In this work, a new method for calculating the effective length of a complex folded cavity is established based on nonlinear regression analysis, and the effect of folding on the effective length of the cavity is evaluated. It is found that any complex folded cavity can typically be divided into multiple separate 90-degree and 180-degree folded cavities. The overall effect of folding on the entire absorber can be determined by calculating the individual fold’s actual change in effective length and then combining these changes. In addition, the actual effective length of the folded cavity is determined by using the resonant frequency obtained from the numerical simulation. The total cavity length, cross-sectional dimensions, and folding ratio of the cavity (the ratio of length before and after the folding location) are selected as variables for numerical simulation to create the data set to derive the nonlinear regression equations of the effective length of 90-degree and 180-degree folded cavities, respectively. The accuracy of the derived mathematical expressions is demonstrated through simulation verification and experimental validations.