Effective Medium Representation of Periodic Designs Based on a Semi-Analytical Approach

An important practical application of an acoustic metamaterial for underwater applications is as a hull coating on marine vessels. Such coatings may be periodic multilayered media comprising alternating layers of two materials, or elastic media with periodic inclusions. This work investigates the use of an effective medium approach to study a 2D periodic design of an elastic medium with soft or rigid inclusions. A semi-analytical approach that combines a differential method and a finite element model of the unit cell of the 2D periodic design is used to obtain the transfer matrix associated with the representative unit cell. Effective properties associated with the unit cell, including the effective speed of sound and the effective mass density, are then derived from the transfer matrix. Finally, the transmission and reflection coefficients of a structure formed by a finite number of unit cells in the direction of sound propagation and immersed in water are computed using the effective medium properties. To assess the validity and accuracy of the method presented here, results for the acoustic performance of the effective medium representation based on the semi-analytical approach are compared with those from direct computation of the 2D design from a finite element model.