Modelling resonant arrays of the Helmholtz type in the time domain
We present a model based on a two-scale asymptotic analysis for resonant arrays of the Helmholtz type, with resonators open at a single extremity (standard resonators) or open at both extremities (double-sided resonators). The effective behaviour of such arrays is that of a homogeneous anisotropic s...
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| Veröffentlicht in: | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2018-02, Vol.474 (2210), p.20170894-20170894 |
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| container_end_page | 20170894 |
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| container_issue | 2210 |
| container_start_page | 20170894 |
| container_title | Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences |
| container_volume | 474 |
| creator | Maurel, Agnès Marigo, Jean-Jacques Mercier, Jean-François Pham, Kim |
| description | We present a model based on a two-scale asymptotic analysis for resonant arrays of the Helmholtz type, with resonators open at a single extremity (standard resonators) or open at both extremities (double-sided resonators). The effective behaviour of such arrays is that of a homogeneous anisotropic slab replacing the cavity region, associated with transmission, or jump, conditions for the acoustic pressure and for the normal velocity across the region of the necks. The coefficients entering in the effective wave equation are simply related to the fraction of air in the periodic cell of the array. Those entering in the jump conditions are related to near field effects in the vicinity of the necks and they encapsulate the effects of their geometry. The effective problem, which accounts for the coupling of the resonators with the surrounding air, is written in the time domain which allows us to question the equation of energy conservation. This is of practical importance if the numerical implementations of the effective problem in the time domain is sought. |
| doi_str_mv | 10.1098/rspa.2017.0894 |
| format | Article |
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A, Mathematical, physical, and engineering sciences</title><addtitle>Proc. R. Soc. A</addtitle><addtitle>Proc Math Phys Eng Sci</addtitle><description>We present a model based on a two-scale asymptotic analysis for resonant arrays of the Helmholtz type, with resonators open at a single extremity (standard resonators) or open at both extremities (double-sided resonators). The effective behaviour of such arrays is that of a homogeneous anisotropic slab replacing the cavity region, associated with transmission, or jump, conditions for the acoustic pressure and for the normal velocity across the region of the necks. The coefficients entering in the effective wave equation are simply related to the fraction of air in the periodic cell of the array. Those entering in the jump conditions are related to near field effects in the vicinity of the necks and they encapsulate the effects of their geometry. The effective problem, which accounts for the coupling of the resonators with the surrounding air, is written in the time domain which allows us to question the equation of energy conservation. 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| source | Jstor Complete Legacy; Alma/SFX Local Collection; JSTOR Mathematics & Statistics |
| subjects | Acoustics Arrays Asymptotic Analysis Energy conservation Engineering Sciences Helmholtz Resonator High-Order Homogenization Mathematical models Mechanics Metamaterial Neck Physics Resonators Solid mechanics Time domain analysis Wave equations |
| title | Modelling resonant arrays of the Helmholtz type in the time domain |
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