## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

(82)

#### 11.4.2.2 Antisymmetric Solution

Subtraction of the ${\sigma }_{yy}$ equations, i.e., Eq. (74)Eq. (75), and addition of the ${\sigma }_{xy}$ equations, i.e., Eq. (76)+Eq. (77), yields

$\begin{array}{l}{A}_{1}\left({\xi }^{2}-{\eta }_{S}^{2}\right)\mathrm{sin}{\eta }_{P}d-{B}_{2}2\xi {\eta }_{S}\mathrm{sin}{\eta }_{S}d=0\hfill \\ {A}_{1}2\xi {\eta }_{P}\mathrm{cos}{\eta }_{P}d+{B}_{2}\left({\xi }^{2}-{\eta }_{S}^{2}\right)\mathrm{cos}{\eta }_{S}d=\frac{\stackrel{˜}{\tau }}{2i\mu }\hfill \end{array}\left(\mathrm{antisymmetric}\mathrm{motion}\right)$ (83)

(83)

In matrix notations, we write

$\left[\begin{array}{ll}\left({\xi }^{2}-{\eta }_{S}^{2}\right)\mathrm{sin}{\eta }_{P}d\hfill & -2\xi {\eta }_{S}\mathrm{sin}{\eta }_{S}d\hfill \\ 2\xi {\eta }_{P}\mathrm{cos}{\eta }_{P}d\hfill & \left({\xi }^{2}-{\eta }_{S}^{2}\right)\mathrm{cos}{\eta }_{S}d\hfill \end{array}$

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required