Natural Frequency of Free Torsional Vibration for Rotor B of Two Rotor System Solution

STEP 0: Pre-Calculation Summary
Formula Used
Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia)/(Distance of Node from Rotor B*Mass Moment of Inertia of Rotor B)))/(2*pi)
f = (sqrt((G*J)/(lB*IB rotor)))/(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 - (Measured in Meter⁴) - Polar Moment of Inertia of shaft is the measure of object resistance to torsion.
Distance of Node from Rotor B - (Measured in Meter) - Distance of Node from Rotor B is a numerical measurement of how far apart objects or points are.
Mass Moment of Inertia of Rotor B - (Measured in Kilogram Square Meter) - Mass moment of inertia of rotor B is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.
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: 0.01 Meter⁴ --> 0.01 Meter⁴ No Conversion Required
Distance of Node from Rotor B: 3.2 Millimeter --> 0.0032 Meter (Check conversion here)
Mass Moment of Inertia of Rotor B: 78.6 Kilogram Square Meter --> 78.6 Kilogram Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
f = (sqrt((G*J)/(lB*IB rotor)))/(2*pi) --> (sqrt((40*0.01)/(0.0032*78.6)))/(2*pi)
Evaluating ... ...
f = 0.200707621868529
STEP 3: Convert Result to Output's Unit
0.200707621868529 Hertz --> No Conversion Required
FINAL ANSWER
0.200707621868529 0.200708 Hertz <-- Frequency
(Calculation completed in 00.004 seconds)

Credits

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

Natural Frequency of Free Torsional Vibration for Rotor B of Two Rotor System
Go Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia)/(Distance of Node from Rotor B*Mass Moment of Inertia of Rotor B)))/(2*pi)
Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System
Go Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia)/(Distance of Node from Rotor A*Mass Moment of Inertia of Rotor A)))/(2*pi)
Mass Moment of Inertia of Rotor A, for Torsional Vibration of Two Rotor System
Go Mass Moment of Inertia of Rotor A = (Mass Moment of Inertia of Mass Attached to Shaft B*Distance of Node from Rotor B)/(Distance of Node from Rotor A)
Mass Moment of Inertia of Rotor B, for Torsional Vibration of Two Rotor System
Go Mass Moment of Inertia of Rotor B = (Mass Moment of Inertia of Mass Attached to Shaft A*Distance of Node from Rotor A)/(Distance of Node from Rotor B)
Distance of Node from Rotor B, for Torsional Vibration of Two Rotor System
Go Distance of Node from Rotor B = (Mass Moment of Inertia of Mass Attached to Shaft A*Distance of Node from Rotor A)/(Mass Moment of Inertia of Rotor B)
Distance of Node from Rotor A, for Torsional Vibration of Two Rotor System
Go Distance of Node from Rotor A = (Mass Moment of Inertia of Mass Attached to Shaft B*Distance of Node from Rotor B)/(Mass Moment of Inertia of Rotor A)

Natural Frequency of Free Torsional Vibration for Rotor B of Two Rotor System Formula

Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia)/(Distance of Node from Rotor B*Mass Moment of Inertia of Rotor B)))/(2*pi)
f = (sqrt((G*J)/(lB*IB rotor)))/(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 for Rotor B of Two Rotor System?

Natural Frequency of Free Torsional Vibration for Rotor B of Two Rotor System calculator uses Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia)/(Distance of Node from Rotor B*Mass Moment of Inertia of Rotor B)))/(2*pi) to calculate the Frequency, The Natural frequency of free torsional vibration for rotor B of two 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 for Rotor B of Two Rotor System using this online calculator? To use this online calculator for Natural Frequency of Free Torsional Vibration for Rotor B of Two Rotor System, enter Modulus of Rigidity (G), Polar Moment of Inertia (J), Distance of Node from Rotor B (lB) & Mass Moment of Inertia of Rotor B (IB rotor) and hit the calculate button. Here is how the Natural Frequency of Free Torsional Vibration for Rotor B of Two Rotor System calculation can be explained with given input values -> 0.200708 = (sqrt((40*0.01)/(0.0032*78.6)))/(2*pi).

FAQ

What is Natural Frequency of Free Torsional Vibration for Rotor B of Two Rotor System?
The Natural frequency of free torsional vibration for rotor B of two 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*J)/(lB*IB rotor)))/(2*pi) or Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia)/(Distance of Node from Rotor B*Mass Moment of Inertia of Rotor B)))/(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, Distance of Node from Rotor B is a numerical measurement of how far apart objects or points are & Mass moment of inertia of rotor B is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.
How to calculate Natural Frequency of Free Torsional Vibration for Rotor B of Two Rotor System?
The Natural frequency of free torsional vibration for rotor B of two 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)/(Distance of Node from Rotor B*Mass Moment of Inertia of Rotor B)))/(2*pi). To calculate Natural Frequency of Free Torsional Vibration for Rotor B of Two Rotor System, you need Modulus of Rigidity (G), Polar Moment of Inertia (J), Distance of Node from Rotor B (lB) & Mass Moment of Inertia of Rotor B (IB rotor). With our tool, you need to enter the respective value for Modulus of Rigidity, Polar Moment of Inertia, Distance of Node from Rotor B & Mass Moment of Inertia of Rotor B and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Frequency?
In this formula, Frequency uses Modulus of Rigidity, Polar Moment of Inertia, Distance of Node from Rotor B & Mass Moment of Inertia of Rotor B. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia)/(Distance of Node from Rotor A*Mass Moment of Inertia of Rotor A)))/(2*pi)
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