SIMPLY SUPPORTED BEAM NATURAL FREQUENCY



Simply supported beam natural frequency calculator to calculate natural frequency of a uniform beam with uniform load w per unit length including beam weight. Beam is simply supported from both ends. The natural frequency formula for simply supported beam is $${ f }_{ n }=\frac { { K }_{ n } }{ 2\pi } \sqrt { \frac { EIg }{ w{ l }^{ 4 } } } $$

Here in the formula, I is area moment of inertia, l is length of the shaft, E is modulus of elasticity and w is uniform load.


Simply Supported Beam Natural Frequency Calculator:

Natural frequency of simply supported beam
 INPUT PARAMETERS
Parameter Value
Modulus of Elasticity [E]
Area Moment of Inertia [I]
Beam length [L]
Uniform load per unit length [w]

Note: Use dot "." as decimal separator.

 


 RESULTS
Parameter Value
First natural frequency [f1] --- Hz
Second natural frequency [f2] ---
Third natural frequency [f3] ---
Forth natural frequency [f4] ---
Fifth natural frequency [f5] ---


List of Equations:

Equation
Natural frequency of simply supported beam with uniform load w per unit length including beam weight [fn]
$${ f }_{ n }=\frac { { K }_{ n } }{ 2\pi } \sqrt { \frac { EIg }{ w{ l }^{ 4 } } } $$

Symbol Parameter
Kn A constant where n refers to the mode of vibration.
Mode 1 - Kn = 9.87
Mode 2 - Kn = 39.5
Mode 3 - Kn = 88.8
Mode 4 - Kn = 158
Mode 5 - Kn =247
I Area moment of inertia
l Length of the shaft
E Modulus of elasticity
w Uniform load

Reference: