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What is the resonant frequency

Fo for the silicon cantilever beam of 2000μm long and 200μm wide and 1.5μm thick? (Data for silicon E = 190 GPa and The density is 2.39 g/cm3)

Mumbai University > Electronics Engineering > Sem 8 > MEMS Technology

Marks: 5M

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Given

w = 200μm

t = 1.5 μm

E = 190 GPa

ρ = 2.39 g/cm3

  = 2.39 x 10-15 kg/ μm


$I = wt^3/12$ = 56.25 μm

Area (A) = w x t

        = 200 x 1.5

= 300 μm2


$f_0 =\frac{3.52}{\pi} \times \sqrt{\frac{E .I}{ρ A L^4}}$

=$1081.46 Khz$