Vibration of a membrane strip with a segment of higher density: analysis of trapped modes

Wang, C. Y.

doi:10.1007/s11012-014-0034-7

Cited by 9 publications

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A different but related problem, concerns the existence of bound states in open geometries, that are not necessarily deformed, but contain local heterogeneities. For the solvable case of an infinite, straight, two-dimensional waveguide, containing a segment of different density, Wang [16] has proved the existence of bound states. Moreover, at least in two dimensions, the problem of studying the spectrum of a deformed waveguide can be reduced to the problem of studying the spectrum of a heterogeneous straight waveguide, by using a suitable conformal map which transforms one domain into the other.…”

Section: Introductionmentioning

confidence: 99%

Weakly bound states in heterogeneous waveguides

2016

View full text Add to dashboard Cite

Abstract. We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the heterogeneity corresponds to a locally denser material, the lowest eigenvalue of the spectrum falls below the continuum threshold and a bound state appears, localized at the heterogeneity. We devise a rigorous perturbation scheme and derive the exact expression for the energy to third order in the heterogeneity.

show abstract

Section: Introductionmentioning

confidence: 99%