Length correction model considering a right-angle bend of Fabry–Pérot sound absorbers

Abstract

Aiming at the problem that the peak frequency of Fabry–Pérot (F–P) resonance metamaterials is shifted to high frequency due to the right-angle bend, we start from the mechanism of the frequency shift caused by the bend and propose a length correction theoretical model. Using the idea of equivalence, the effect of a corner is the first equivalent to the effective density. Then, the change in effective density is equivalent to the effective length, and the theoretical derivation is completed. This model can guide the length design of the F–P tube. Moreover, it can be used to predict the peak frequency of the F–P tube with a right-angle bend if its geometric dimensions are known. Through the analysis from theory, simulation, and experiment of two samples, the accuracy of the length correction theoretical model is verified. Additionally, by the power dissipation density and the dissipated energies, it is determined that the fundamental reason for the frequency shift is that the right-angle bend changes the distribution of power dissipation density in the tube. The work in this paper is of guiding significance for the frequency prediction and length design of F–P tubes.