  We study the Cauchy problem associated with the equations governing a fluid
loaded plate formulated on either the line or the half-line. We show that in
both cases the problem can be solved by employing the unified approach to
boundary value problems introduced by on of the authors in the late 1990s. The
problem on the full line was analysed by Crighton et. al. using a combination
of Laplace and Fourier transforms. The new approach avoids the technical
difficulty of the a priori assumption that the amplitude of the plate is in
$L^1_{dt}(R^+)$ and furthermore yields a simpler solution representation which
immediately implies the problem is well-posed. For the problem on the
half-line, a similar analysis yields a solution representation, but this
formula involves two unknown functions. The main difficulty with the half-line
problem is the characterisation of these two functions. By employing the
so-called global relation, we show that the two functions can be obtained via
the solution of a complex valued integral equation of the convolution type.
This equation can be solved in closed form using the Laplace transform. By
prescribing the initial data $\eta_0$ to be in $H^3(R^+)$, we show that the
solution depends continuously on the initial data, and hence, the problem is
well-posed.
