Sound transmission loss of plate-type metastructures: Semi-analytical modeling, elaborate analysis, and experimental validation

Abstract

Recent studies on plate-type metastructures have shown promising applications in low-frequency sound insulation, as they possess a low-frequency sound transmission loss (STL) that is considerably higher than that derived from the mass law. To design a plate-type metastructure for a sound insulation application, three problems are worth exploring: 1) how to predict efficiently the STL of the metastructure, 2) how to understand its unusual STL behavior, and 3) how to design its parameters to obtain a high STL at a target frequency and achieve a broad frequency band of high STL without increasing the mass. The purpose of this work is to address these problems by investigating a plate-type metastructure that is simply constructed using a periodic array of mass blocks attached to a thin host plate. For the first problem, a semi-analytical method is proposed for efficient prediction of normal, oblique, and diffuse STL based on fast retrieval of dynamic surface mass density using a considerably reduced structural finite element model and without having to include the acoustic field. This method is validated based on comparisons with an existing numerical method and reported experimental data. For the second problem, the mechanisms of unusual STL behavior are revealed by analyzing dynamic surface mass density as well as Bloch wave dispersion and Bloch modes. The third problem is addressed by conducting an elaborate parametric analysis that provides straightforward guidelines for adjusting structural parameters to tune the STL peak frequency as well as offering general guidelines for designing multiple parameters to achieve a broader frequency band of high diffuse STL with a given surface mass density. A design guideline for improving STL bandwidth is experimentally validated through measurements of two specimens designed and fabricated with identical surface mass densities. Because the considered plate-type metastructure is simple yet instructive, these investigations and findings are of fundamental and practical interest to the design of sound insulation metastructures.