TORSIONAL VIBRATION OF A SHAFT
Torsional vibration of a shaft calculator was developed to calculate natural frequency of a uniform shaft with a concentrated end mass. Shaft is fixed from one end and the other end
is free (cantilevered shaft). The formulas used for vibration of unifrom shaft calculations are given in the "List of
Equations" section.
Calculator:
Note: Use dot "." as decimal separator.
RESULTS 
Parameter 
Symbol 
Value 
Unit 
Polar second moment of area of uniform shaft 
K 



Mass moment of inertia of uniform shaft 
J_{s} 



First torsional natural frequency of the system 
f_{1} 


Hz 
Definitions:
Modulus of rigidity (modulus of elasticity in shear): The rate of change of unit shear stress with respect to unit shear strain for the condition of pure shear within the proportional limit. Typical values Aluminum 6061T6: 24 GPa, Structural Steel: 79.3 GPa.
Polar Moment of Inertia: A geometric property of cross section. Measure of ability how a beam resists torsion.
List of Equations:
Parameter/Condition 
Symbol 
Equation 
Polar second moment of area of a hollow shaft 
K 

Mass moment of inertia of a hollow shaft 
J_{s} 

First torsional natural frequency of the system (Approximately) 
f_{1} 

Symbol 
Parameter 
m_{s} 
Shaft mass 
J 
Mass moment of inertia of the point mass 
l 
Length of the shaft 
r_{i} 
Hollow shaft inner radius 
r_{o} 
Shaft outer radius 