The samples investigated here consist of two type 
aluminum plates, bonded by 
adhesive of 
thickness.
The properties of Al2024 are 
and for the adhesive
. The
boundary between the adhesive and the adherend plate is usually composed of
two very thin layers. One is the Aluminum oxide which has about 100 nm
thickness and can be disregarded for our purpose and the second layer is the
primer with about 
thickness and 
.
Guided (undamped) waves can be searched by restricting the analysis to the
real axis of k. It turned out that the degree of bonding can be determined
by measuring the velocity of the guided wave [9].
, for the first mode.
Fig. 2 shows the influence of interfacial stiffness on the velocity of the
first ultrasonic wave mode.
is normalized such that 
reduces to
the case of delamination, while 
represents the case of good bonding.
For low frequencies, 
, the difference between the
various cases reaches its maximum. For very high frequencies, 
, the power of the wave is localized mainly in the adhesive layer and
the contribution from the boundary is negligible. A point of interest is
which is the place where the thickness of the layer is
equal to 
where 
is the ultrasonic
wavelength.
This is the point of the mechanical fundamental mode resonance of the adhesive
layer, as will be shown again later. Here, the velocity is equal for all
possible values of . Thus for a determination of the bond strength
one should operate away from this region, preferably around
and 
.
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