NATURAL FREQUENCY OF A UNIFORM BEAM WITH FIXED ENDS


Fixed fixed beam natural frequency calculator to calculate natural frequency of a uniform beam with both ends fixed. The natural frequency formulas used for calculations are given below the calculator.


Fixed - Fixed Beam Natural Frequency Calculator:


 INPUT PARAMETERS
Parameter Value
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 center load
Parameter Value
First natural frequency [f1] --- Hz
Uniform load w per unit length including beam weight
Natural frequency of fixed beam with Uniform Load
Parameter Value
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 and center load
Parameter Value
First natural frequency [f1] --- Hz


List of Equations:

Parameter Equation
First natural frequency of fixed beam with center load M, beam weight negligible [f1 ] $${ f }_{ 1 }=\frac { 13.86 }{ 2\pi } \sqrt { \frac { EIg }{ M{ l }^{ 3 } } } $$
Natural frequency of fixed beam with uniform load w per unit length including beam weight [fn] $${ f }_{ n }=\frac { { K }_{ n } }{ 2\pi } \sqrt { \frac { EIg }{ w{ l }^{ 4 } } } $$
First natural frequency of fixed beam with uniform load w per unit length plus a center load M (approximately) [f1] $${ f }_{ 1 }=\frac { 13.86 }{ 2\pi } \sqrt { \frac { EIg }{ M{ l }^{ 3 }+0.383w{ l }^{ 4 } } } $$

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: