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

(211)

yields the in-plane displacement field across the thickness of a flexing beam in the form

$u(x,z,t)=-z\frac{\partial }{\partial x}\hat{w}{e}^{i(\gamma x-\omega t)}=-i\gamma z\hat{w}{e}^{i(\gamma x-\omega t)}=-i\gamma zw(x,t)$ (212)

(212)

The particle motion described by Eqs. (211) and (212) is shown in Figure 5.9. It is apparent that the particle motion is elliptical, with the ellipse aspect ratio varying from maximum at the surface to zero in the middle of the transverse thickness.

Figure 5.9 Simulation of flexural waves. ...