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Based on the basic equations of elastic waves in general media, the general form of dual variables equations for plane elastic waves in general elastic media are developed by the transformation of matrix and vector operation. The general form of dual variables equations are generally suitable not only for isotropic and perfect elastic media, but also for anisotropic and viscoelastic media, and adapt to the coupling of various wave types. Putting the elastic coefficients of stiffness matrix of specific medium layer in the general form of dual variables equations, the dual variables equations of the specific medium layer can directly be obtained. The general solving methods for elastic waves problems are presented based on the solutions of dual variables equations. Finally, solving the eigenvalue problems of anisotropic media of cubic system and isotropic media are demonstrated, and the effectiveness and universal applicability of the general form of dual variables equations are indicated.

The General Form of Dual Variables Equations for Elastic Waves in General Elastic Media Layers and Its Applications