skip to main content

Title: Umov-Mandelshtam radiation conditions in elastic periodic waveguides

We study settings of the problem of elasticity theory on wave propagation in an elastic periodic waveguide with radiation conditions at infinity. We present a mathematical theory for energy radiation conditions based on Mandelshtam's energy principle and the Umov-Poynting vector, as well as using the technique of weighted spaces with detached asymptotics and the energy transfer symplectic form. We establish that in a threshold situation, that is, when standing and polynomial elastic Floquet waves appear, the well-known limiting absorption principle, in contrast to the energy principle that is being applied, cannot identify the direction of the wave's motion. Bibliography: 37 titles. (paper)
Authors:
 [1]
  1. St. Petersburg State University, Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences, St. Petersburg (Russian Federation)
Publication Date:
OSTI Identifier:
22364931
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 7; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ABSORPTION; ASYMPTOTIC SOLUTIONS; ELASTICITY; ENERGY TRANSFER; FLOQUET FUNCTION; PERIODICITY; POLYNOMIALS; POYNTING THEOREM; WAVE PROPAGATION; WAVEGUIDES