Properties of superresonant systems of spherical scatterers

Systems of identical precisely spaced bubbles or similar monopole scatterers in water-e.g., inflated balloons or thin-walled shells-insonified at frequencies
\omega_{SR}
dose to their fundamental radial resonance
\omega_{0}
(bubble) frequency may themselves display resonance modes or superresonances (SR's) [1]. Ordinary single-bubble resonances magnify the local free-field pressure amplitude
p_{1}
by a factor
(ka)^{-1}
,
a
being the radius and
k
the wavenumber in water: for air bubbles or balloons in water, this factor is of the order of 70. Under SR conditions each member of the system amplifies the local free-field amplitude by a further factor of order
(ka)^{-1}
. Depending upon geometry and other constraints, the pressure field
P_{SR}
on the surface and in the interior of each scatterer will then be in the range of
10^{3}p_{1}
to
5 \times 10^{3} p_{1}
. This paper investigates the sensitivity of this phenomenon to small departures from the ideal model. In particular, it examines the effect of small differences in scatter positioning and volumes in the context of an SR system consisting of two bubbles/balloons close to the boundary of a thin elastic plate overlying a fluid half-space. It is found that, to observe the SR phenomenon, radii and positions should be controlled to within approximately 1/2 percent.
P_{SR}
is also sensitive to the angle of incidence of the plane wave train. For the simple system examined here, this sensitivity is considerable for either flexural wave trains or volume acoustic waves incident upon the bubble/ balloon pair (doublet). Practical uses of the phenomenon may range from the design of passive high-
Q
acoustical filter/amplifiers and acoustical lenses to improved source efficiencies.