To build a 20 µm wide fixed-free cantilever beam with a force constant of 10 N/m and a resonant frequency of 10 kHz out of single crystal silicon, find the desired length and thickness of the cantilever beam. The Young’s modulus of silicon is 120 GPa. The density of the silicon material is 2330 kg/m3.

To build a 20 µm wide fixed-free cantilever beam with a force constant of 10 N/m and a resonant frequency of 10 kHz out of single crystal silicon, find the desired length and thickness of the cantilever beam. The Young’s modulus of silicon is 120 GPa. The density of the silicon material is 2330 kg/m3.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter3: Transient Heat Conduction

Section: Chapter Questions

Problem 3.4P

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To construct a cantilever beam 40 µm wide, with a force constant of 20 N/m, and a resonance frequency of 20 kHz from single-crystalline silicon, find the length and thickness of the cantilever beam. Young's modulus for silicon is 120 GPa. The density of the silicon material is 2330 Kg/m3.
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This is a follow up to my question and the answer you submitted. The equation you used for J is wrong, not sure how you got J=π32×Do4-Di4, the equation should be J=π/2×ro4-ri4 which is J=pi/2(50^4-40^4) = 5.8e+6 mm^4
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