On Well-Posedness of Scattering Problems in a Kirchhoff--Love Infinite Plate
Laurent Bourgeois, Christophe Hazard
Abstract
We address scattering problems for impenetrable obstacles in an infinite elastic Kirchhoff--Love two-dimensional plate. The analysis is restricted to the purely bending case and the time-harmonic regime. Considering four types of boundary conditions on the obstacle, well-posedness for those problems is proved with the help of a variational approach: (i) for any wave number $k$ when the plate is clamped, simply supported, or roller supported; (ii) for any $k$ except a discrete set when the plate is free (this set is finite for convex obstacles).
Topics & Concepts
Obstacle problemMathematical analysisMathematicsObstacleRegular polygonBending of platesBoundary (topology)Boundary value problemScatteringSet (abstract data type)BendingHarmonic functionInfinite setGeometryPhysicsComputer scienceOpticsProgramming languageLawThermodynamicsPolitical scienceNumerical methods in engineeringAdvanced Mathematical Modeling in EngineeringGeophysical Methods and Applications