For this case,
, so . The two
eigenvectors are , with no
dependence on the fluid properties. However, the eigenvalues continue
to be functions of the fluid properties. This seems to be a
rather special case, but again considering the quasi-isotropic limit, we
find that ,where is Poisson's ratio and *E* is Young's modulus.
For this combination of the parameters to vanish for special values
does not appear to violate any of the well-known constraints (such as
positivity, etc.) on these parameters. For example, if ,the term depending on the fluid properties clearly makes a negative
contribution, which might be large enough to cancel the contribution
from the solid. But, for now, this case seems rather artificial, so
we will not consider it further here.

5/23/2004