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

(127)

Substituting $u(t)=\hat{u}\cos \omega t$, we write

$E=T(t)+V(t)=\frac{1}{2}m{\omega }^2{\hat{u}}^2{\sin }^2\omega t+\frac{1}{2}k{\hat{u}}^2{\cos }^2\omega t$ (128)

(128)

Recalling Eq. (15), i.e., $k={\omega }_n^{2}m$, we can write Eq. (128) as

$E=T(t)+V(t)=\frac{1}{2}m{\hat{u}}^2({\omega }^2{\sin }^2\omega t+{\omega }_n^2{\cos }^2\omega t)$ (129)

(129)

Derivation of the Equation of Motion by ...