NATURAL FREQUENCY OF A UNIFORM BEAM WITH FIXED ENDS

This calculator has been developed to calculate natural frequency of a uniform beam with both ends fixed. The formulas used for fixed beam natural frequency calculations are given in the "List of Equations" section.


Calculator:

 INPUT PARAMETERS
Parameter Symbol Value Unit
Modulus of Elasticity E
Area Moment of Inertia I
Beam length L
Uniform load per unit length w
Center load M

Note: Use dot "." as decimal separator.

 


 RESULTS
Center load M, beam weight negligible
Natural frequency of fixed beam with Uniform Load
Parameter Symbol Value Unit
First natural frequency f1 --- Hz
Uniform load w per unit length including beam weight
Natural frequency of fixed beam with Uniform Load
Parameter Symbol Value Unit
First natural frequency f1 --- Hz
Second natural frequency f2 ---
Third natural frequency f3 ---
Forth natural frequency f4 ---
Fifth natural frequency f5 ---
Uniform load w per unit length plus a center load M (approximately)
Natural frequency of fixed beam with Uniform Load
Parameter Symbol Value Unit
First natural frequency f1 --- Hz


List of Equations:

Parameter/Condition Symbol Equation
First natural frequency of fixed beam with center load M, beam weight negligible f1  Equation for  natural frequency of a fixed beam with center load M
Natural frequency of fixed beam with uniform load w per unit length including beam weight fn Equation for  natural frequency of a fixed beam
First natural frequency of fixed beam with uniform load w per unit length plus a center load M (approximately) f1 Equation for  natural frequency of a fixed beam with uniform load w per unit length plus a center load M

Symbol Parameter
Kn A constant where n refers to the mode of vibration.
Mode 1 - Kn = 22.4
Mode 2 - Kn = 61.7
Mode 3 - Kn = 121
Mode 4 - Kn = 200
Mode 5 - Kn =299
I Area moment of inertia
l Length of the shaft
E Modulus of elasticity
w Uniform load
M Center load

Reference: