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.

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