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THE FEUTEX TOOLKIT

Cantilever First Bending Frequency

Estimate the first transverse mode of a uniform unloaded cantilever.

Mechanical workspace● Runs in your browser
01 Your input
02 Your result
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Formulaf₁=β₁²/(2πL²)√(EI/ρA), β₁≈1.875104.
Sources and model references

Worked example

Inputs

Beam length
1 m
Young modulus
200000000000 Pa
Second moment
1e-08 m⁴
Density
7800 kg/m³
Cross-sectional area
0.0001 m²

Expected results

First bending natural frequency
28.33600239 Hz
Beam mass
0.78 kg

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter every input in the labeled units; use measured or independently specified properties.
  2. Check the stated model assumptions before calculating.
  3. Interpret the output as a model estimate and verify it independently for the intended application.

Try this example

{
  "length": 1,
  "e": 200000000000,
  "i": 1e-8,
  "rho": 7800,
  "area": 0.0001
}

Accuracy and scope

Uniform Euler–Bernoulli beam with perfect clamp, no added tip mass, axial load or shear-deformation correction. Educational engineering estimate only; not structural or safety certification, equipment selection, or operating recommendations.

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This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.