Author(s): Utban Ahmed; Muhammad Waqar; Saber Nasraoui; Moez Louati; Mohamed S. Ghidaoui
Linked Author(s): Moez LOUATI, Mohamed S. Ghidaoui, Muhammad Waqar
Keywords: Metamaterials; Local resonances; Effective medium theory
Abstract: Locally resonant materials or metamaterials, engineered structures with properties not typically found in nature, have revolutionized the control and manipulation of waves in various media, including fluids [1]. These materials consist of locally resonant elements, or simply resonators, arranged periodically at a subwavelength scale within a host medium (solid, fluid, or composite). Unlike conventional resonances, the resonances of the resonators are highly localized and consequently, they are called subwavelength/local resonances. Thus, when a wave propagating in the host medium encounters these closely packed resonators, the wave undergoes multiple resonant scattering which drastically alters the phase, speed, and direction of the wave. This multiple resonant scattering in metamaterials enables the wave control at a deep subwavelength scale and as a result, these materials exhibit properties such as pass and stop bands, negative density, negative bulk modulus, negative and zero refraction and tunneling among others [1]. With these exotic properties, metamaterials have found many intriguing applications such as wave bending, trapping, super-lensing, super-resolution, and cloaking. It needs to be noted that the localized resonances are different from the well-known Bragg resonances, for which the spatial periodicity is a rudimentary requirement. The local resonances of the resonators are free from such requirement as they only depend upon the structural properties of the resonators. By way of example, we analytically derive a dispersion relation for the waves in a fluid conveying pipe which is periodically loaded with Helmholtz resonators. In the subwavelength regime, we obtain a simple closed form solution for the effective wavenumber of the system and show the conditions pertaining to the completely imaginary effective wavenumber, marking the existence of band gaps. We further discuss the origin and physical interpretation of the band gaps by discussing the concepts of negative density and negative bulk modulus. Some Fluid Mechanical Applications of Metamaterial: Given the exceptional control at the subwavelength scale by metamaterials, potential applications include: (i) bending of water and acoustic waves in fluid channels and conduits to optimize transmission[1][2]; (ii) cloaking of entities in fluid environments to mitigate scattering of both water and acoustic waves[1][3]; (iii) promoting unidirectional wave propagation using graded metamaterials[1]; (iv) enhancing coastal protection against wave forces[3]; (v) harvesting wave energy utilizing localized resonances[1]; (vi) managing and dissipating waterhammer waves in hydraulic systems; (vii) precise manipulation of fluid flows; (viii) achieving drag-free flows; and (ix) employing superlensing and super-resolution techniques for precise source localization in fluid domains. Methods: To illustrate the fundamental formulation of a metamaterial system, consider the fluid filled pipe connected to periodically spaced Helmholtz Resonators (HRs) which are commonly used locally resonant elements. It is easy to observe in Fig. (1a) that the system has a repeating entity which corresponds to the length
Year: 2024