A comparison of time domain boundary conditions for acoustic waves in wave guides

Banks, Harvey Thomas; Propst, Georg; Silcox, R. J.

doi:10.1090/qam/1388015

Cited by 1 publication

(1 citation statement)

References 13 publications

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“…We quote the work by Russell, 21 Majda, 22 Lagnese, 23 Banks et al, 24 Darmawijoyo and Van Horssen, 7 Cox and Zuazua. 6 Rideau 4 has treated the 1D case with a (unique) resistive termination, giving explicitly a scalar product (see also Ref.5).…”

Section: Riesz Basis Of the Modesmentioning

confidence: 99%

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

Kergomard

Debut

Matignon

2006

The Journal of the Acoustical Society of America

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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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