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

(264)

Equation (264) has a nontrivial solution $C_1\ne 0$ only if

$\cos \gamma l=0$ (265)

(265)

Substitution of Eq. (187) $z=\gamma l$ into Eq. (265) yields the eigenvalue equation

$\cos z=0$ (266)

(266)

which has the roots

$z=\frac{\pi }{2},3\frac{\pi }{2},5\frac{\pi }{2},\dots \mathrm{or}{z}_j=(2j-1)\frac{\pi }{2},j=1,2,3,\dots$ (267)