Embedded trapped modes for obstacles in two-dimensional waveguides
problem.
M. McIver, C.M. Linton, P. McIver, J. Zhang & R. Porter
Quart. J. Mech Appl. Maths 54(2), 273--293.
In this paper we investigate the existence of embedded trapped
modes for symmetric obstacles which are placed on the centreline of
a two-dimensional acoustic waveguide. Modes are sought which are
antisymmetric about the centreline of the channel but which have
frequencies that are above the first cut-off for antisymmetric wave
propagation down the guide. In the terminology of spectral theory this
means that the eigenvalue associated with the trapped mode is embedded
in the c ontinuous spectrum of the relevant operator.
A numerical procedure, based on a boundary integral technique is developed
to search for embedded trapped modes for bodies of general shape.
In addition two approximate solutions for trapped modes are found; the
first is for long plates on the centreline of the channel and the second
is for slender bodies which are perturbations of plates perpendicular to
the guide walls. It is found that embedded trapped modes do not exist
for arbitrary symmetric bodies but if an obstacle is defined by two
geometrical parameters then branches of trapped modes may be obtained by
varying both of these parameters simultaneously. The plates themselves
are found to correspond to the end points of these branches.
Download PDF