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We consider a two-dimensional infinitely long acoustic waveguide formed by two parallel lines containing an arbitrarily shaped obstacle. The existence of trapped modes that are the eigenfunctions of the Laplace operator in the corresponding domain subject to Neumann boundary conditions was proved...
In a series of papers by Hill and co-workers, a number of exact integrals are derived for plane strain, plane stress, and axially symmetric deformations of an isotropic, incompressible Varga elastic material. Here we show for more general plane strain deformations with transverse stretch that the...