Table 1.

Effect of added mass on the resonant frequency shift of the cantilever beam reported by Yi et al. [91]. Reused with permission from [91].

Description	Added Point Mass at the Tip	Added Mass Distributed on a Narrow Strip	Added Mass Distributed over the Entire Beam	Size Reduction
Schematic
Resonant frequency shift	$\frac{\Delta f}{\Delta m}\cong \frac{{\nu }_n^2}{4\pi }\frac{1}{L^{3}W}\left(\frac{1}{0.236\sqrt{12}\rho }\sqrt{\frac{E}{\rho }}\right)$		$\frac{\Delta f}{\Delta m}\cong \frac{{\nu }_n^2}{4\pi }\frac{1}{L^{3}W}\left(\frac{1}{\sqrt{12}\rho }\sqrt{\frac{E}{\rho }}\right)$	$\frac{\Delta f}{\Delta m}\left(\alpha L,\alpha W\right)={\alpha }^{-4}\frac{\Delta f}{\Delta m}\left(L,W\right)$