An investigation into the direct control of the effective material properties of a fluid medium using active noise control

Abstract

Acoustic metamaterials are subwavelength-engineered structures that can exhibit behaviour not seen in conventional materials. The effective material properties for acoustic metamaterials are the bulk modulus and density. Negative effective material properties can create band gaps, where wave propagation is forbidden. Hence, acoustic metamaterials can achieve high levels of noise control performance. Active control has been combined with passive acoustic metamaterials to enhance the level of attenuation or broaden the bandwidth of the band gap. However, the width of the band gaps for these materials are still limited by the use of resonators. This study will investigate whether active control can be employed to directly minimise the effective material properties, which requires an optimization procedure. To begin to understand this optimization problem, the effective material properties have been calculated as a function of the real and imaginary parts of the control source strength at various frequencies for monopole and dipole sources. The resulting error surfaces demonstrate that the two configurations could achieve negative effective material properties; however, the cost functions are not always convex without constraints. Therefore, to adaptively manipulate the effective material properties using an active control system would require the development of an advanced optimization procedure.