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Engineering · Vibration & Rotating Systems

Uniform Beam First Natural Frequency Calculator

Estimate the first Euler–Bernoulli bending frequency of a uniform simply supported or cantilever beam from entered properties.

Engineering · Vibration & Rotating Systems

Enter the engineering model

Explicit properties, geometry, units and assumptions
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Visual modelSchematic · not to scale
Vibration & Rotating Systems: beamSimple visual explanationA simplified diagram showing the relationship represented by the selected calculator mode. It is explanatory and not a fabrication, safety or scale drawing.first ideal uniform-beam bending modesupport condition changes β₁
The diagram explains the selected relationship only. Dimensions, symbols and proportions are illustrative; use the entered values and stated assumptions for the calculation.

Keep every unit basis, sign convention, property source and idealization consistent. Values stay in this browser.

Engineering calculation result

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Understand the dynamic model

What this calculator is for

Estimate the first Euler–Bernoulli bending frequency of a uniform simply supported or cantilever beam from entered properties. It exists to make the selected ideal model, its inputs, and its limits visible before the result is used elsewhere.

1Match the physical system to the displayed mass, stiffness, damping and support topology.
2Use one consistent force, length, mass and time basis.
3Compare the intermediate frequency or ratio outputs before interpreting amplitude.

Visual explanation

The tailored schematic separates inertia, elastic restraint, damping or excitation so the governing relationship can be read as a physical model rather than an unexplained formula.

The governing relationship

f₁=β₁²/(2πL²)√(EI/(ρA)); β₁=π simply supported and 1.875104 cantilever.

Keep the boundary visible

Uniform slender beam, small bending, no added mass, shear deformation, rotary inertia, damping or support flexibility.

Quick guide

How to use this calculator

  1. Choose the analysis mode that matches the physical model before entering values.
  2. Enter properties, geometry, loads, states and coefficients from one consistent unit and sign convention.
  3. Use the intermediate outputs to audit the relationship, then retain the stated idealization before applying it.

Calculation method

Transparent engineering model

f₁=β₁²/(2πL²)√(EI/(ρA)); β₁=π simply supported and 1.875104 cantilever.

The calculator evaluates only the declared relationship and preserves visitor-entered assumptions rather than selecting materials, factors, components or standards.

Worked example

Worked example

The support condition changes β₁ and therefore the first ideal bending frequency even with identical beam properties.

f₁=β₁²/(2πL²)√(EI/(ρA)); β₁=π simply supported and 1.875104 cantilever.

Supported inputs

Precision and limits

Analysis, not approval

Uniform slender beam, small bending, no added mass, shear deformation, rotary inertia, damping or support flexibility.

Standards and properties

Material properties, allowable values, load combinations, safety factors, correlations, manufacturer data, codes and jurisdictional requirements are not supplied automatically.

Units and precision

Use one consistent unit basis. Results retain working precision but cannot be more accurate than the entered measurements and properties.

Privacy

Entered engineering values and results stay in this browser and are not sent to analytics or third parties.