# 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:

 INPUT PARAMETERS Parameter Symbol Value Unit Density of shaft ps g/cm^3 kg/m^3 lb/in^3 Shaft outer diameter do mm cm m inch ft Shaft inner diameter di Shaft length l Modulus of rigidity G GPa psi*10^6 Mass moment of inertia of end mass J g*mm^2 kg*m^2 lb*in^2 lb*ft^2

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

 RESULTS Parameter Symbol Value Unit Polar second moment of area of uniform shaft K --- mm^4 cm^4 inch^4 ft^4 Mass moment of inertia of uniform shaft Js --- g*mm^2 kg*m^2 lb*in^2 lb*ft^2 First torsional natural frequency of the system f1 --- 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 6061-T6: 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 Js First torsional natural frequency of the system (Approximately) f1

 Symbol Parameter ms Shaft mass J Mass moment of inertia of the point mass l Length of the shaft ri Hollow shaft inner radius ro Shaft outer radius