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This paper investigates the scattering of biharmonic waves by aone-dimensional periodic array of cavities embedded in an infinite elastic thinplate. The transparent boundary conditions are introduced to formulate theproblem from an unbounded domain to a bounded one. The well-posedness of theassociated variational problem is demonstrated utilizing the Fredholmalternative theorem. The perfectly matched layer (PML) method is employed toreformulate the original scattering problem, transforming it from an unboundeddomain to a bounded one. The transparent boundary conditions for the PMLproblem are deduced, and the well-posedness of its variational problem isestablished. Moreover, exponential convergence is achieved between the solutionof the PML problem and that of the original scattering problem.

Convergence of the PML method for the biharmonic wave scattering problem in periodic structures