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Formula for Free Resonating Frequency of Cantilever to the Deflection

 
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Aug25-07, 09:16 PM   #1
 

Formula for Free Resonating Frequency of Cantilever to the Deflection

Is there a formula relating the free resonating frequency of a cantilever to its deflection? Thanks!
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Aug26-07, 11:43 PM   #2
 
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The resonant frequency is a function of material and geometric properties of the beam and is independent of the deflection.

For a cantilever beam of uniform cross-section,

[tex]f=\frac{1}{2\pi} \sqrt {\frac{8EI}{\rho Al^4}} [/tex]

I: moment of inertia (depends on cross section)
E: Young's modulus
[itex]\rho[/itex]: density
A: cross-section area
[itex]l[/itex]: length
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