The Generalized Routh Equations in the Plate Theory of th Order and their Use in Problems of Normal Wave Dispersion in Heterogeneous Waveguides.

Autor: Zhavoronok, S. I., Kurbatov, A. S., Rabinskiy, L. N.
Zdroj: Lobachevskii Journal of Mathematics; Jul2022, Vol. 43 Issue 7, p2010-2018, 9p
Abstrakt: Based on the variational formulation of the theory of th order of plates as two-dimensional continuum systems, the equations of motion as well as the constitutive equations for a transversally inhomogeneous plate are obtained, resolved with respect to the first derivatives of generalized displacements along one of the spatial coordinates and appropriate generalized forces and written in a form similar to the known Routh equations of classical mechanics. The obtained problem formulation allows one to use both orthogonal polynomials and compact functions corresponding to the semi-analytical finite element method as a basis. The application of the proposed new equations of the th order plate theory to the problem of normal wave dispersion in an elastic isotropic functionally graded plane layer leads to a linear formulation of the spectral problem with respect to the wave number and, consequently, allows us to construct dispersion branches of propagating and evanescent modes of normal waves. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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