Nonlocal dynamics of dissipative phononic fluids
Author(s)
Lafarge, Denis; Duclos, Aroune; Nemati, Navid; Lee, Yoon Kyung; Fang, Xuanlai
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We describe the nonlocal effective properties of a two-dimensional dissipative phononic crystal made by periodic arrays of rigid and motionless cylinders embedded in a viscothermal fluid such as air. The description is based on a nonlocal theory of sound propagation in stationary random fluid/rigid media that was proposed by Lafarge and Nemati [Wave Motion 50, 1016 (2013)WAMOD90165-212510.1016/j.wavemoti.2013.04.007]. This scheme arises from a deep analogy with electromagnetism and a set of physics-based postulates including, particularly, the action-response procedures, whereby the effective density and bulk modulus are determined. Here, we revisit this approach, and clarify further its founding physical principles through presenting it in a unified formulation together with the two-scale asymptotic homogenization theory that is interpreted as the local limit. Strong evidence is provided to show that the validity of the principles and postulates within the nonlocal theory extends to high-frequency bands, well beyond the long-wavelength regime. In particular, we demonstrate that up to the third Brillouin zone including the Bragg scattering, the complex and dispersive phase velocity of the least-attenuated wave in the phononic crystal which is generated by our nonlocal scheme agrees exactly with that reproduced by a direct approach based on the Bloch theorem and multiple scattering method. In high frequencies, the effective wave and its associated parameters are analyzed by treating the phononic crystal as a random medium.
Date issued
2017-06Department
Massachusetts Institute of Technology. Department of Mechanical EngineeringJournal
Physical Review B
Publisher
American Physical Society
Citation
Nemati, Navid; Lee, Yoonkyung E.; Lafarge, Denis; Duclos, Aroune and Fang, Nicholas. "Nonlocal dynamics of dissipative phononic fluids." Physical Review B 95, 224304 (June 2017): 1-15 © 2017 American Physical Society
Version: Final published version
ISSN
2469-9950
2469-9969