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

(67)

where ${\xi }^{*}$ is a real number. To understand the meaning of Eq. (67), let us substitute it into the general expression Eq. (34); we get

$u_z(x,y,t)=h(y)e^{i(\xi x-\omega t)}=h(y)e^{i(i{\xi }^{*}x)}{e}^{-i\omega t}$ (68)

(68)

i.e.,

$u_z(x,y,t)=\left[h(y)e^{-{\xi }^{*}x}\right]e^{-i\omega t}$ (69)

(69)

Equation (69) describes an evanescent¹ wave, which has a decaying amplitude and only exists close to the excitation ...