Abstract
The primary objective of acoustic metamaterial research is to design subwavelength systems that behave as effective materials with novel acoustical properties. One such property couples the stress–strain and the momentum–velocity relations. This response is analogous to bianisotropy in electromagnetism, is absent from common materials, and is often referred to as Willis coupling after J.R., Willis, who first described it in the context of the dynamic response of heterogeneous elastic media. This work presents two principal results: first, experimental and theoretical demonstrations, illustrating that Willis properties are required to obtain physically meaningful effective material properties resulting solely from local behaviour of an asymmetric one-dimensional isolated element and, second, an experimental procedure to extract the effective material properties from a one-dimensional isolated element. The measured material properties are in very good agreement with theoretical predictions and thus provide improved understanding of the physical mechanisms leading to Willis coupling in acoustic metamaterials.
Highlights
The primary objective of acoustic metamaterial (AMM) research is to design subwavelength systems that behave as effective materials and display novel acoustical properties[1,2,3]
Examples of such novel properties include zero or negative dynamic mass density[4] and bulk modulus[5], chirality[6] and a more general material response that couples strain and momentum fields, as well as stress and velocity fields[7,8]. The latter response was initially described by Willis[9] and is often referred to as Willis coupling. This behaviour may be described as acoustic bianisotropy due to its mathematical similarities to bianisotropy in electromagnetism[8,10]
Reciprocal Willis coupling results from two different physical phenomena: local coupling associated with microstructural asymmetry and nonlocal coupling associated with finite phase change across a unit cell and multiple scattering between spatially separated heterogeneities[12,13,14,15,16,17,18]
Summary
The primary objective of acoustic metamaterial research is to design subwavelength systems that behave as effective materials with novel acoustical properties. The primary objective of acoustic metamaterial (AMM) research is to design subwavelength systems that behave as effective materials and display novel acoustical properties[1,2,3] Examples of such novel properties include zero or negative dynamic mass density[4] and bulk modulus[5], chirality[6] and a more general material response that couples strain and momentum fields, as well as stress and velocity fields[7,8]. For lossy systems it becomes difficult to distinguish between the two contributors to Willis coupling, but becomes easier when nonlocal effects are rendered negligible by considering an acoustically small metamaterial element that is isolated rather than part of an ensemble of mutually interacting elements Under these conditions and with a properly designed experiment, coupling due to nonlocal effects may be neglected and the Willis coupling coefficients must be equal to each other, that is c~ 1⁄4 c, by reciprocity[12]. It is possible to represent a material response resulting from subwavelength heterogeneities and non-local effects with constitutive relations that are not of the form provided in equations (1) and (2)
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
