Online Beam Natural Frequency Calculator

This active web form can be used to calculate the first 2 modes of a general beam configuration.  Up to 24 different beam segments can be used with each having different section and area properties including weight density.  Concentrated weights can also be added.  Boundaries include free, simple support and fixed slope.  Both vertical and rotational springs can also be used.

Output includes the first 2 mode frequencies in Hz and the respective mode shapes.  A gravitational constant must be defined.  All dimensional units must be consistent with each other and Hz.

A uniform beam of length = 24 inches, E = 30,000,000 psi, I = .25 in⁴, A = .28167 in², weight density of 0.3 lb/in³ gave the following results compared to theoretical values:

Cantilevered:
Model f₁ = 179.8; f₂ = 1124.4 versus theory of f₁ = 179.9; f₂ = 1127.5 Hz

Fixed End/Simple Supported End:
Model f₁ = 789.0; f₂ = 2556.9 versus theory of f₁ = 789.0; f₂ = 2556.7 Hz

Fixed End/Fixed End:
Model f₁ = 1144.9; f₂ = 3159.7 versus theory of f₁ = 1144.9; f₂ = 3155.8 Hz

Reference: Theory of Vibration with Applications, W. T. Thomson, 4th Edition.

Simply change or add values to any of the white cells and the frequencies are automatically updated.




The following screenshot is a more complex configuration and with all of the features used.

Complex Beam Configuration.