Beam Natural Frequency Calculator Form
Example Data Table
| Case | Support | Length | Section | Material | Approx. First Mode |
|---|---|---|---|---|---|
| Lab test beam | Cantilever | 2.0 m | 50 × 8 mm | Steel | 1.63 Hz |
| Light frame member | Simply supported | 1.5 m | 40 × 6 mm | Aluminum | 6.11 Hz |
| Machine shaft model | Fixed-fixed | 1.2 m | Ø 30 mm | Steel | 61.76 Hz |
Formula Used
Natural circular frequency:
ωn = (βn² / L²) × √(EI / (ρA))
Natural frequency in hertz:
fn = ωn / (2π)
Damped frequency estimate:
fd = fn × √(1 - ζ²)
Rectangular section properties:
A = b × h and I = b × h³ / 12
Circular section properties:
A = πd² / 4 and I = πd⁴ / 64
Where: βn is the modal constant for the support condition, L is beam length, E is Young’s modulus, I is the second moment of area, ρ is density, A is cross-sectional area, and ζ is damping ratio.
This model is intended for uniform, slender beams with small deflections. It does not include rotary inertia, shear deformation, taper, cracks, variable sections, or large attached masses.
How to Use This Calculator
- Select the beam support condition that matches your setup.
- Enter the beam length and choose the correct length unit.
- Pick a section shape, then enter width and height or diameter.
- Choose a material preset or type your own modulus and density.
- Select how many modes to calculate and which mode to highlight.
- Add an optional damping ratio to estimate damped frequency.
- Press Calculate Frequency to show results above the form.
- Review the summary cards, modal table, Plotly graph, and export buttons.
Frequently Asked Questions
1) What theory does this calculator use?
It uses Euler-Bernoulli beam vibration theory for uniform beams. The frequency depends on support condition, length, flexural rigidity, and mass per unit length.
2) Why does support condition matter so much?
Support condition changes the modal constant βn. A fixed beam is usually stiffer than a simply supported or cantilever beam, so its natural frequencies are higher.
3) Which mode should I check first?
The first mode is often most important because it usually has the largest response in practical systems. Higher modes matter when excitation or geometry makes them relevant.
4) How do dimensions affect frequency?
Longer beams lower frequency sharply. Increasing section depth usually raises frequency because the second moment of area increases rapidly with depth.
5) Can I use circular and rectangular sections?
Yes. The calculator supports both shapes and automatically applies the correct area and second moment of area formulas for each section.
6) What does damping ratio change here?
Damping does not change the undamped natural frequency shown in the main modal solution. It adds a damped-frequency estimate so you can compare lightly damped behavior.
7) When is this model less accurate?
Accuracy drops for thick beams, composite laminates, tapered members, cracked sections, large attached masses, very high modes, or cases where shear deformation becomes important.
8) What units should I enter?
Use any supported length and section units, but keep them consistent with the physical geometry. Young’s modulus is entered in GPa and density in kg/m³.