# 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.

 INPUT PARAMETERS Parameter Value 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 Value First natural frequency [f1] --- Hz Uniform load w per unit length including beam weight 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) Parameter Value First natural frequency [f1] --- Hz

### Fixed Fixed Beam Natural Frequency Formula:

 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