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Resonance modes in a one-dimensional medium with two purely resistive boundaries: Calculation methods, orthogonality, and completeness

Kergomard, Jean and Debut, Vincent and Matignon, Denis Resonance modes in a one-dimensional medium with two purely resistive boundaries: Calculation methods, orthogonality, and completeness. (2006) The Journal of the Acoustical Society of America, 119 (3). 1356-1367. ISSN 0001-4966

(Document in English)

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Official URL: http://dx.doi.org/10.1121/1.2166709


Studying the problem of wave propagation in media with resistive boundaries can be made by searching for “resonance modes” or free oscillations regimes. In the present article, a simple case is investigated, which allows one to enlighten the respective interest of different, classical methods, some of them being rather delicate. This case is the one-dimensional propagation in a homogeneous medium having two purely resistive terminations, the calculation of the Green function being done without any approximation using three methods. The first one is the straightforward use of the closed-form solution in the frequency domain and the residue calculus. Then, the method of separation of variables (space and time) leads to a solution depending on the initial conditions. The question of the orthogonality and completeness of the complex-valued resonance modes is investigated, leading to the expression of a particular scalar product. The last method is the expansion in biorthogonal modes in the frequency domain, the modes having eigenfrequencies depending on the frequency. Results of the three methods generalize or∕and correct some results already existing in the literature, and exhibit the particular difficulty of the treatment of the constant mode.

Item Type:Article
Additional Information:Thanks to Acoustical Society of America editor. The definitive version is available at http://scitation.aip.org/ The original PDF of the article can be found at The Journal of the Acoustical Society of America: http://scitation.aip.org/content/asa/journal/jasa/119/3/10.1121/1.2166709
HAL Id:hal-01374263
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Aix-Marseille Université - AMU (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole nationale supérieure des Télécommunications - ENST (FRANCE)
Other partners > Télécom Paris (FRANCE)
Other partners > Université de Provence - Aix-Marseille I (FRANCE)
Other partners > Ecole Centrale Marseille (FRANCE)
Other partners > Université de la Méditerranée - Aix-Marseille II (FRANCE)
Laboratory name:
Deposited On:30 Sep 2016 08:17

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