A silicon MEMS cantilever is a uniform rectangular beam of length and thickness

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Vibrating bodies, musical and architectural acoustics · Vibrating bodies, musical and architectural acoustics

Bending, Ringing, Breaking and Flowing, Ch Vibrations of rods, beams and plates

Problem

A silicon MEMS cantilever is a uniform rectangular beam of length

L = 350\,\mathrm{\mu m}

and thickness

h = 3.5\,\mathrm{\mu m}

, clamped at one end and free at the other, made of silicon with

E = 170\,\mathrm{GPa}

and

\rho = 2330\,\mathrm{kg\,m^{-3}}

. ((a)) State the clamped-free frequency equation and the value of its lowest root

\beta_1L

. ((b)) Using

I/A = h^2/12

for a rectangular cross-section (the width cancels), find the fundamental resonance frequency of this cantilever.

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