Analogy of TE waveguide and vibrating plate with sliding edge condition and exact solutions

Abstract

Presented herein is a proof that the TE (transverse electric) waveguide problem is analogous to the vibration problem of thin plates with zero slope and zero twisting moment at the freely sliding edges in the vertical (transverse) direction. This analogy is confirmed because of the mathematical similarity of the governing equations and the boundary conditions of the two problems. We also present exact solutions for these two analogous problems for various domain shapes. The exact solutions are very useful for checking the validity, convergence and accuracy of numerical methods for solving the Helmholtz equation. © 2013 Copyright Taylor and Francis Group, LLC.