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The solution for the case when the top surface is free and the bottom surface is
rigid can be deduced from the odd solution of the rigidrigid case. The problem is
defined by

(67) 
subject to boundary condition
The boundary conditions at the mid height for the odd solution is the (69).
Accordingly an odd solution for the rigidrigid boundary at depth provides
solution for the rigidfree boundary for a depth . Thus using the stability
results from the rigidrigid case, we have
and 
(70) 
[Note: From
in dimensional form, we have ( is the
scaling length) as the nodimensional wave number.]
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20030116