Table 6.

Relative frequency shift of cantilever and doubly clamped beam resonators with surface stress and geometric effects reported by Karabalin et al. [203]. A normalized load $\overline{\sigma }=(1-\nu ){\sigma }_s^T/(Eh)$ is applied and ${\sigma }_s^T$ is an applied surface stress.

Resonator Structure	Relative Frequency Shift $\Delta f/f_0$
	Stress Effect	Geometric Effect
Cantilever beam	$-0.042\nu (b/L){(b/h)}^2\overline{\sigma }$	$[(1+2\nu )/(1-\nu )]\overline{\sigma }$
Doubly clamped beam	$0.1475{(L/h)}^2\overline{\sigma }$	$\{(1+2\nu )(1+\nu )/[2(1-\nu )]\}\overline{\sigma }$