# 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 GPa psi*10^6 Area Moment of Inertia I mm^4 cm^4 inch^4 ft^4 Beam length L mm cm m inch ft Uniform load per unit length w N/mm lbf/in Center load M N kN lbf

###### Note: Use dot "." as decimal separator.

 RESULTS Center load M, beam weight negligible Parameter Symbol Value Unit First natural frequency f1 --- Hz Uniform load w per unit length including beam weight 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) 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 Natural frequency of fixed beam with uniform load w per unit length including beam weight fn First natural frequency of fixed beam with uniform load w per unit length plus a center load M (approximately) f1

 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