Natural Frequency of Free Torsional Vibration of Single Rotor System Solution

STEP 0: Pre-Calculation Summary
Formula Used
Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia of Shaft)/(Length of Shaft*Moment of inertia of Shaft)))/(2*pi)
f = (sqrt((G*Jshaft)/(L*Ishaft)))/(2*pi)
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Frequency - (Measured in Hertz) - Frequency is the number of times something happens in a particular period.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity represents the elastic coefficient that causes lateral deformation when a shear force is applied to a body. It is an indicator of a body's rigidity.
Polar Moment of Inertia of Shaft - (Measured in Meter⁴) - Polar Moment of Inertia of Shaft is the measure of object resistance to torsion.
Length of Shaft - (Measured in Meter) - The Length of Shaft is the distance between two ends of shaft.
Moment of inertia of Shaft - (Measured in Kilogram Square Meter) - Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.
STEP 1: Convert Input(s) to Base Unit
Modulus of Rigidity: 40 Newton per Square Meter --> 40 Pascal (Check conversion here)
Polar Moment of Inertia of Shaft: 10 Meter⁴ --> 10 Meter⁴ No Conversion Required
Length of Shaft: 7000 Millimeter --> 7 Meter (Check conversion here)
Moment of inertia of Shaft: 100 Kilogram Square Meter --> 100 Kilogram Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
f = (sqrt((G*Jshaft)/(L*Ishaft)))/(2*pi) --> (sqrt((40*10)/(7*100)))/(2*pi)
Evaluating ... ...
f = 0.120309828385084
STEP 3: Convert Result to Output's Unit
0.120309828385084 Hertz --> No Conversion Required
FINAL ANSWER
0.120309828385084 0.12031 Hertz <-- Frequency
(Calculation completed in 00.020 seconds)

Credits

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National Institute Of Technology (NIT), Hamirpur
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2 Free Torsional Vibrations of Single Rotor System Calculators

Natural Frequency of Free Torsional Vibration of Single Rotor System
Go Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia of Shaft)/(Length of Shaft*Moment of inertia of Shaft)))/(2*pi)
Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System
Go Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft

Natural Frequency of Free Torsional Vibration of Single Rotor System Formula

Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia of Shaft)/(Length of Shaft*Moment of inertia of Shaft)))/(2*pi)
f = (sqrt((G*Jshaft)/(L*Ishaft)))/(2*pi)

What is the difference between free and forced vibration?

Free vibrations involve no transfer of energy between the vibrating object and its surroundings, whereas forced vibrations occur when there's an external driving force and thus transfer of energy between the vibrating object and its surroundings.

How to Calculate Natural Frequency of Free Torsional Vibration of Single Rotor System?

Natural Frequency of Free Torsional Vibration of Single Rotor System calculator uses Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia of Shaft)/(Length of Shaft*Moment of inertia of Shaft)))/(2*pi) to calculate the Frequency, The Natural frequency of free torsional vibration of single rotor system formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force. Frequency is denoted by f symbol.

How to calculate Natural Frequency of Free Torsional Vibration of Single Rotor System using this online calculator? To use this online calculator for Natural Frequency of Free Torsional Vibration of Single Rotor System, enter Modulus of Rigidity (G), Polar Moment of Inertia of Shaft (Jshaft), Length of Shaft (L) & Moment of inertia of Shaft (Ishaft) and hit the calculate button. Here is how the Natural Frequency of Free Torsional Vibration of Single Rotor System calculation can be explained with given input values -> 0.12031 = (sqrt((40*10)/(7*100)))/(2*pi).

FAQ

What is Natural Frequency of Free Torsional Vibration of Single Rotor System?
The Natural frequency of free torsional vibration of single rotor system formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force and is represented as f = (sqrt((G*Jshaft)/(L*Ishaft)))/(2*pi) or Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia of Shaft)/(Length of Shaft*Moment of inertia of Shaft)))/(2*pi). Modulus of Rigidity represents the elastic coefficient that causes lateral deformation when a shear force is applied to a body. It is an indicator of a body's rigidity, Polar Moment of Inertia of Shaft is the measure of object resistance to torsion, The Length of Shaft is the distance between two ends of shaft & Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.
How to calculate Natural Frequency of Free Torsional Vibration of Single Rotor System?
The Natural frequency of free torsional vibration of single rotor system formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force is calculated using Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia of Shaft)/(Length of Shaft*Moment of inertia of Shaft)))/(2*pi). To calculate Natural Frequency of Free Torsional Vibration of Single Rotor System, you need Modulus of Rigidity (G), Polar Moment of Inertia of Shaft (Jshaft), Length of Shaft (L) & Moment of inertia of Shaft (Ishaft). With our tool, you need to enter the respective value for Modulus of Rigidity, Polar Moment of Inertia of Shaft, Length of Shaft & Moment of inertia of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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