Dual variables system analysis for plane SH wave

Dual variables system is a new systematic methodology for analysis of dynamic systems, and can be applied in plane SH wave problems. In dual variables system, uniform SH wave and inhomogeneous SH wave can be analyzed by the general methods. Corresponding to the solutions of Hamilton dual equation, there are three forms of solution for SH wave: eigenvector expansion solution, modal expansion solution and transfer form solution. Based on the eigenvector expansion solution, reflection problem, transmission problem and boundary value problem of SH waves are solved, reflection coefficients and transmission coefficients are given. In dual variables system, the analysis and calculation methods of SH wave problems obtain the same results as the traditional methods, and the methods are intuitional and simple, moreover, the intrinsic relationships among different forms of solution of SH wave can be revealed.