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Torsional vibration calculation of a shaft to find 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).

Torsional Vibration Calculator of a Shaft:

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INPUT PARAMETERS
Parameter	Value
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]	全程露脸东北老女 全程露脸东北老女 ,星球大战克隆人战争第五季 星球大战克隆人战争第五季
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.

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RESULTS
Parameter	Value全程露脸东北老女 全程露脸东北老女 ,星球大战克隆人战争第五季 星球大战克隆人战争第五季
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.

Torsional Vibration Equations:

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

Supplements:

• Vibration Calculators

Reference:

• Young, W. C., Budynas, R. G.(2002). Roark's Formulas for Stress and Strain . 7nd Edition, McGraw-Hill, Chapter 16 , pp 767 - 768
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