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International Journal of Fluid Mechanics Research

ISSN Print: 1064-2277
ISSN Online: 2152-5102

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v26.i5-6.130
pages 732-741

Extension of the Method of Cross Sections to the Problem of Wave Propagation in an Elastic Layer with Smoothly Varying Parameters

B. V. Galanenko
Kiev Polytechnic Institute, Kiev, Ukraine


The method of cross sections, usually employed in investigating liquid acoustic waveguides, is extended to the two-dimensional problem of wave motion of an elastic isotropic layer whose material and shape parameters change smoothly in the direction of wave propagation. The cross section operator, specified on a set four-dimensional vector-valued functions, whose components are the horizontal and vertical displacements, the component of the rotor and the divergence, is defined. Orthogonality equations for the operator's eigenfunctions are obtained and the equations of coupled modes are derived. The eigenvalues of a waveguide in the form of an elastic wedge are investigated.