dorsal/arxiv
View SchemaResonance modes in a 1D medium with two purely resistive boundaries: calculation methods, orthogonality and completeness
| Authors | Jean Kergomard, Vincent Debut, Denis Matignon |
|---|---|
| Categories | |
| ArXiv ID | physics/0411238 |
| URL | https://arxiv.org/abs/physics/0411238 |
| DOI | 10.1121/1.2166709 |
| Journal | Journal of the Acoustical Society of America 119 (2006) 1356-1367 |
Abstract
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 1D 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.
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"abstract": "Studying the problem of wave propagation in media with resistive boundaries\ncan be made by searching for \"resonance modes\" or free oscillations regimes. In\nthe present article, a simple case is investigated, which allows one to\nenlighten the respective interest of different, classical methods, some of them\nbeing rather delicate. This case is the 1D propagation in a homogeneous medium\nhaving two purely resistive terminations, the calculation of the Green function\nbeing done without any approximation using three methods. The first one is the\nstraightforward use of the closed-form solution in the frequency domain and the\nresidue calculus. Then the method of separation of variables (space and time)\nleads to a solution depending on the initial conditions. The question of the\northogonality and completeness of the complex-valued resonance modes is\ninvestigated, leading to the expression of a particular scalar product. The\nlast method is the expansion in biorthogonal modes in the frequency domain, the\nmodes having eigenfrequencies depending on the frequency. Results of the three\nmethods generalize or/and correct some results already existing in the\nliterature, and exhibit the particular difficulty of the treatment of the\nconstant mode.",
"arxiv_id": "physics/0411238",
"authors": [
"Jean Kergomard",
"Vincent Debut",
"Denis Matignon"
],
"categories": [
"physics.class-ph"
],
"doi": "10.1121/1.2166709",
"journal_ref": "Journal of the Acoustical Society of America 119 (2006) 1356-1367",
"title": "Resonance modes in a 1D medium with two purely resistive boundaries: calculation methods, orthogonality and completeness",
"url": "https://arxiv.org/abs/physics/0411238"
},
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