Investigation on dynamic effective parameters of perforated thin-plate acoustic metamaterials

In this paper, dynamic effective parameters of mass-type and stiffness-type perforated thin-plate acoustic metamaterials (PAMs) are investigated by numerical simulations and experiments to fundamentally reveal formation mechanisms of acoustic characteristics. The perforated mass thin-plate acoustic metamaterial (PMAM) is proposed as a mass-type PAM, the effective mass densities (EMDs) of unperforated mass thin-plate acoustic metamaterial (UMAM) and PMAM are calculated by direct method and retrieval method, and formation mechanisms of unusual values are analyzed by EMD definition and simulated fields. A new anti-resonance frequency is produced by perforation, at where EMD is much higher than the static bulk-averaged values. In particular, EMD of PMAM is equal to that of UMAM in parallel with the air hole when perforation radius is small, but the relationship is broken when perforation radius is big. The perforated frame thin-plate acoustic metamaterial (PFAM) is proposed as a stiffness-type PAM, the EMDs calculated in numerical simulations and experiments verify the perforation effects revealed in mass-type PAM. In addition, the impacts of perforation parameters on EMD show variation trends of resonance and anti-resonance frequencies are different in two types of PAMs because perforations change system mass in the PMAM but change stiffness in the PFAM. Thus this work is of guiding significance to understand the acoustic characteristics of PAM from the perspective of dynamic effective parameters.