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Formula for Free Resonating Frequency of Cantilever to the Deflection

  1. Aug 25, 2007 #1
    Is there a formula relating the free resonating frequency of a cantilever to its deflection? Thanks!
     
  2. jcsd
  3. Aug 26, 2007 #2

    Gokul43201

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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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