Structural Health Monitoring with Piezoelectric Wafer Active Sensors, 2nd Edition

(402)

The homogeneous algebraic system (402) accepts nontrivial solutions only if its determinant has value zero, i.e.,

$\left|\begin{array}{cc}-\sin \gamma l+\sinh \gamma l& -\cos \gamma l+\cosh \gamma l\\ -\cos \gamma l+\cosh \gamma l& \sin \gamma l+\sinh \gamma l\end{array}\right|=0$ (403)

(403)

Expansion and simplification of Eq. (403) yields

$\cos \gamma l\cosh \gamma l-1=0$ (404)

(404)

Introduce the notation

$z=\gamma l$ (405)

(405)

Substitution of Eq. (405) into Eq. ...