Dual variables system analysis for plane elastic waves

Regarding displacement components and the corresponding stress components as dual variables, elastodynamic problems can be steered to Hamiltonian dual variables system. For normal incidence problems of simple harmonic plane elastic waves, the decoupling of P-, SV- and SH-waves corresponds to decomposition of dual equation, and as one-dimensional wave, each decoupled wave has the corresponding dual equation with same equation forms, analyzing and solving methods. Wave properties, analyzing and solving methods of plane elastic waves can be all embodied in dual variables system. The eigenvalue problems of dual equation can solve wave number, wave velocity and wave impedance of medium. The eigenvector expansion solutions of dual equation are suited to analysis of the reflection and transmission of elastic waves, the modal expansion solutions of dual equation are suited to the modal analysis of layer structure, and stratified media have the transfer matrix methods based on the transition form solutions of dual equation.