The theoretical and experimental studies of the ultrasonic scattering
by cylindrical shells filled with air and immersed in water have shown
, on the backscattering spectra, large amplitude variations. These var
iations are related to an interface wave called the ''Scholte-Stoneley
wave'' or ''A wave''. The resonances of this wave are detected in a f
requency window that depends on the radius ratio (inner radius b/outer
radius alpha). They are observed for cylindrical shells with a radius
ratio greater than 0.6. This wave that propagates in the water around
the pipe is still not very well known in spite of the investigations
which have been devoted to it. This numerical study is concerned with
the evolution with frequency of different resonances for cylindrical s
hells with the radius ratio between 0.2 and 0.95. The interaction betw
een the flexural wave A(0) in the shell and the creeping wave in the f
luid around the pipe, called the Stoneley wave in a thick shell, and w
ith a pole near the pole of the Franz 1 wave for a rigid cylinder in t
he complex plane defined by the Sommerfeld-Watson transform, is studie
d in greater detail. The dispersion curves of the phase velocity for t
hese waves are presented. They show a repulsive area between the two c
urves. This area is translated toward the high frequencies when the ra
dius ratio tends towards 1. This phenomenon is related to the contact
condition at the liquid/shell interface. To verify it, another paramet
er of the contact condition is modified: the density ratio.