EXISTENCE THEOREMS FOR TRAPPED MODES

被引:280
作者
EVANS, DV
LEVITIN, M
VASSILIEV, D
机构
[1] HERIOT WATT UNIV, DEPT MATH, EDINBURGH EH14 4AS, MIDLOTHIAN, SCOTLAND
[2] UNIV SUSSEX, SCH MATH & PHYS SCI, BRIGHTON BN1 9QH, E SUSSEX, ENGLAND
关键词
D O I
10.1017/S0022112094000236
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
A two-dimensional acoustic waveguide of infinite extent described by two parallel lines contains an obstruction of fairly general shape which is symmetric about the centreline of the waveguide. It is proved that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction. Mathematically, this trapped mode is related to an eigenvalue of the Laplace operator in the waveguide. The proof makes use of an extension of the idea of the Rayleigh quotient to characterize the lowest eigenvalue of a differential operator on an infinite domain.
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页码:21 / 31
页数:11
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