  This paper investigates the scattering of biharmonic waves by a
one-dimensional periodic array of cavities embedded in an infinite elastic thin
plate. The transparent boundary conditions are introduced to formulate the
problem from an unbounded domain to a bounded one. The well-posedness of the
associated variational problem is demonstrated utilizing the Fredholm
alternative theorem. The perfectly matched layer (PML) method is employed to
reformulate the original scattering problem, transforming it from an unbounded
domain to a bounded one. The transparent boundary conditions for the PML
problem are deduced, and the well-posedness of its variational problem is
established. Moreover, exponential convergence is achieved between the solution
of the PML problem and that of the original scattering problem.
