Analytical and numerical study on absorption of viscoelastic multilayers with variable cross section and cavity

Abstract

Polymeric layers or multilayers with air cavities or solid particles have considerable attenuation properties and can be tailored to have acoustic impedance close to water. So, many underwater sound absorbers are made from such multilayer structures. In this work, first, we present a transfer matrix method (TMM) based on force equilibrium to be used for variable cross-section viscoelastic multilayers with cavities. The method can be used for layers with various cavity designs; also, the outer boundary can be conical or any other axisymmetric shape. The formulation is derived for different outer impedance-matched boundary conditions. The study of anechoic coatings with periodic holes is then studied as a special case of the developed TMM. In this regard, the difference between the present formulation and related literature is explained and the TMM results are compared with numerical simulations which are performed using COMSOL. Moreover, the effect of cavity shape and bulk loss factor on the echo reduction properties of the coatings are investigated. It is concluded that for small cavity sizes and with an abrupt change of multilayer cross sections, the echo reduction values are more dependent on bulk loss factor, especially near the resonance frequency.