Question

Just need the third question, thank you!

4. (20) Cantilever beam problem. A silicon cantilever of length 500 um, width 50 um and thickness 2 um is subject to a uniform distributed transverse load qo. a). Find the tip deflection, and calculated an effective spring constant for this beam. b). For a load which produces a tip deflection of 2 um, calculate the maximum stress at the support. c). Estimate the resonant frequency of the beam. Then, use COMSOL to verify your Ik calculations. (You may check the first Eigen frequency and use f 2π k for comparison.) 1 = to get m

Answer 1

Resonance frequency of the combe written an f=t си 211 EI M 12 for first natural frequency en= 1.875 E = Modulus of elasticity of silicon=170 X10 Pa I. Moment of inertia of the beam cross-section to bh² tax 50 x (23 x & rm4 to : (23 x 1024 m4 -23 -12 = 3.33x10 M = Men per unit Length = lbh = 2329 x 50 x 2 XLO e Density of silicon= 2329 ng/m3 r dum2 tom2 - Length of the cantilever = 2.328x16-7 500 mm= 500 x 10-6 5x159 1.8752 fa 24 x (5x10-97² 170x101x 3.3341023 2.32 g x 10-7 11039,81 HE

Analytical calculation gives resonant frequency 11039.81 Hz (first natural frequency).

Using COMSOL, first natural frequency is 11112.08 Hz.