Viscothermal Losses in Double-Negative Acoustic Metamaterials


Metamaterials are artificial structures capable of exhibiting properties not found in natural media.  They are based on subwavelength units that can be engineered to meet specific parameters, which opened the door to the proposal of novel devices and the observation of interesting phenomena like negative refraction. Acoustic metamaterials with negative bulk modulus or negative mass density have deserved much attention during the last decade. Double-negative structures (where both parameters are simultaneously negative) were also reported, although only a few have been experimentally demonstrated.

Professor Vicente Cutanda Henríquez at Technical University of Denmark in collaboration with Dr. Víctor M. García-Chocano and Professor José Sánchez-Dehesa at Universitat Politècnica de València in Spain report the influence of viscothermal losses in acoustic metamaterials based on rigid structures. Although viscothermal phenomena are often negligible, it is demonstrated that the associated losses can suppress the predicted double-negative behavior of the metamaterial. The research work is now published in journal Physical Review Applied.

The authors report simulations based on the Boundary Element Method (BEM), which has been implemented including acoustic viscous and thermal losses to create the metamaterial models. The BEM with losses is based on the Kirchhoff decomposition of the linearized Navier-Stokes equations with no flow. The BEM formulation is validated against an equivalent solution using the Finite Element Method (FEM) with losses, as implemented in the COMSOL software package. The BEM model, which in this case is less computationally heavy, is employed in the remaining calculations, which include a very fine frequency resolution, down to 2,5 Hz, and the scaling of the setup to up to 20 times its original size.

The unit cell of the metamaterial consists of a cavity drilled into a waveguide. In addition, a rigid cylinder is placed at the center of the cavity surrounded by eight rigid fins defining a metafluid shell. The results obtained are consistent with the reported experimental data.

The research demonstrates that losses have paramount relevance at the frequencies where double-negative parameters are theoretically expected. This result is present even when the dimensions of the samples are increased. It is concluded that artificial structures based on fin-based rigid elements are not suitable for the implementation of double-negative metamaterials. The authors propose developing efficient absorbers based on the absorptive properties of these type of double-negative metamaterials.

Viscothermal Losses in Double-Negative Acoustic Metamaterials. Advances in Engineering
The photograph on the top shows the designed double-negative metamaterial, which has been engineered using 3D printing. Graph (a) represents pressure values obtained when a sound wave with a plane wavefront propagates without attenuation inside the metamaterial when no visco-thermal losses are considered. However, when visco-thermal losses are taken into account, graph (b) shows how the impinging wave is totally attenuated in the first two rows of the metamaterial. The strong enhancement of visco-thermal losses in these corrugated rigid structures are explained in terms of the huge values attained by the pressure due to the embedded resonances.

About the author

José Sánchez-Dehesa got his PhD in Physics from the Autonomous University of Madrid in 1982. Since October 2003 he is full professor at the Department of Electronic Engineering in the Universitat Politècnica de València where he leads the Wave Phenomena Group. He has been working in different topics in the theory of semiconductors, low dimensional structures and optical devices.

His recent interest is focused in the propagation of sound through artificial structures like phononic crystals and acoustic metamaterials. Particularly, he has developed acoustic barriers for broadband noise and omnidirectional absorbers based on metamaterials. Also, he has demonstrated novel structures for acoustic cloaking in two and three dimensions. In the topic of acoustic metamaterials, he has been involved in homogenization theories and in engineering artificial structures with negative bulk modulus and negative mass density.

His research has been continuously supported by national and international agencies like the Office of Naval Research (USA), the Spanish Ministry of Economy and the European Union. He is Fellow of the American Acoustical Society “for his contributions to the theory and development of acoustic metamaterials”. He coauthored about 200 articles published in international journals and books.

About the author

Vicente Cutanda Henriquez has a degree in Telecommunication Engineering by the Polytechnical University of Madrid, and a Ph.D. in Acoustics by the Technical University of Denmark. After his Ph.D., he worked in acoustic metrology at the National Centre keeping measurement standards in Mexico. He continued his career as an assistant professor at the University of Vigo (Spain), and later as an associate professor, first at the University of Southern Denmark and currently at the Technical University of Denmark (DTU), where he is part of the Centre for Acoustic-Mechanical Micro Systems (CAMM), a research group within DTU sponsored by the Danish hearing aid companies.

His main research interest is numerical modeling in acoustics, where he has developed efficient models implementing acoustic viscous and thermal losses in fluids based on the Boundary Element Method. He is interested in modeling acoustic transducers and other acoustic devices. Lately, he has become interested in the modeling and understanding of intricate structures such as metamaterials and cloaking devices including losses. He has scientific publications corresponding to the research areas just outlined.

About the author

Víctor Manuel García-Chocano studied Telecommunication Engineering and obtained a master degree in Electronic Engineering from the Polytechnic University of Valencia. He worked at the Wave Phenomena Group of this university and obtained a PhD degree in Acoustics in 2015, for which he received an Extraordinary Doctoral Award.

His research is focused on the propagation of sound waves through artificial structures. He developed two and three-dimensional acoustic cloaks for the concealment of objects to sound waves. He also investigated new structures for the enhancement of sound absorption. These activities leaded to the development of traffic noise barriers based on sonic crystals. He took part in the research of acoustic metamaterials exhibiting negative parameters and unusual phenomena such as negative refraction, tunneling and funneling. These works were mainly funded by the Office of Naval Research (USA), the Spanish Ministry of Public Works and the Spanish Ministry of Economy.

He is currently working as a R&D Engineer in a private company. His work is mainly focused on electronics, although he is involved in additional research activities including systems of wireless power transfer, magnetic sensors based on giant magnetoimpedance and the study of Wood anomalies in sonic crystals.


Henríquez VC, García-Chocano VM, Sánchez-Dehesa J. Viscothermal losses in double-negative acoustic metamaterials. Physical Review Applied. 2017 Jul 25; 8(1):014029.


Go To Physical Review Applied

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