Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System Calculator

✖Modulus of Rigidity is the measure of the rigidity or stiffness of a material, which is a critical parameter in torsional vibration analysis of mechanical systems.ⓘ Modulus of Rigidity [G]			+10% -10%
✖Polar Moment of Inertia is a measure of an object's resistance to torsional deformation, which is a twisting force that causes rotation around a longitudinal axis.ⓘ Polar Moment of Inertia [J]			+10% -10%
✖Distance of Node From Rotor A is the length of the line segment from a node to the axis of rotation of Rotor A in a torsional system.ⓘ Distance of Node From Rotor A [l_A]			+10% -10%
✖Mass Moment of Inertia of Rotor A is a measure of the rotor's resistance to changes in its rotation rate, influencing torsional vibration behavior.ⓘ Mass Moment of Inertia of Rotor A [I_A']			+10% -10%

✖Frequency is the number of oscillations or cycles per second of a torsional vibration, typically measured in hertz (Hz), characterizing the vibration's repetitive motion.ⓘ Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System [f]

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Natural Frequency of Free Torsional Vibration for Rotor A 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 A*Mass Moment of Inertia of Rotor A)))/(2*pi)
f = (sqrt((G*J)/(l_A*I_A')))/(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 oscillations or cycles per second of a torsional vibration, typically measured in hertz (Hz), characterizing the vibration's repetitive motion.
Modulus of Rigidity - (Measured in Pascal) - Modulus of Rigidity is the measure of the rigidity or stiffness of a material, which is a critical parameter in torsional vibration analysis of mechanical systems.
Polar Moment of Inertia - (Measured in Meter⁴) - Polar Moment of Inertia is a measure of an object's resistance to torsional deformation, which is a twisting force that causes rotation around a longitudinal axis.
Distance of Node From Rotor A - (Measured in Meter) - Distance of Node From Rotor A is the length of the line segment from a node to the axis of rotation of Rotor A in a torsional system.
Mass Moment of Inertia of Rotor A - (Measured in Kilogram Square Meter) - Mass Moment of Inertia of Rotor A is a measure of the rotor's resistance to changes in its rotation rate, influencing torsional vibration behavior.

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: 0.00164 Meter⁴ --> 0.00164 Meter⁴ No Conversion Required
Distance of Node From Rotor A: 14.4 Millimeter --> 0.0144 Meter (Check conversion here)
Mass Moment of Inertia of Rotor A: 8 Kilogram Square Meter --> 8 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = (sqrt((G*J)/(l_A*I_A')))/(2*pi) --> (sqrt((40*0.00164)/(0.0144*8)))/(2*pi)

Evaluating ... ...

f = 0.120100775527955

STEP 3: Convert Result to Output's Unit

0.120100775527955 Hertz --> No Conversion Required

FINAL ANSWER

0.120100775527955 ≈ 0.120101 Hertz <-- Frequency

(Calculation completed in 00.021 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Free Torsional Vibrations of Rotor Systems » Mechanical » Free Torsional Vibrations of Two Rotor System » Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System

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National Institute Of Technology (NIT), Hamirpur

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< Free Torsional Vibrations of Two Rotor System Calculators

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

LaTeX 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

LaTeX 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)

Distance of Node from Rotor B, for Torsional Vibration of Two Rotor System

LaTeX 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

LaTeX 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 A of Two Rotor System Formula

LaTeX 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)
f = (sqrt((G*J)/(l_A*I_A')))/(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 A of Two Rotor System?

Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System calculator uses Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia)/(Distance of Node From Rotor A*Mass Moment of Inertia of Rotor A)))/(2*pi) to calculate the Frequency, Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System formula is defined as the rate at which the rotor A of a two-rotor system vibrates freely when twisted and then released, measuring the system's natural tendency to oscillate at a specific frequency. Frequency is denoted by f symbol.

How to calculate Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System using this online calculator? To use this online calculator for Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System, enter Modulus of Rigidity (G), Polar Moment of Inertia (J), Distance of Node From Rotor A (l_A) & Mass Moment of Inertia of Rotor A (I_A') and hit the calculate button. Here is how the Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System calculation can be explained with given input values -> 0.120101 = (sqrt((40*0.00164)/(0.0144*8)))/(2*pi).

FAQ

What is Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System?

Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System formula is defined as the rate at which the rotor A of a two-rotor system vibrates freely when twisted and then released, measuring the system's natural tendency to oscillate at a specific frequency and is represented as f = (sqrt((G*J)/(l_A*I_A')))/(2*pi) or Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia)/(Distance of Node From Rotor A*Mass Moment of Inertia of Rotor A)))/(2*pi). Modulus of Rigidity is the measure of the rigidity or stiffness of a material, which is a critical parameter in torsional vibration analysis of mechanical systems, Polar Moment of Inertia is a measure of an object's resistance to torsional deformation, which is a twisting force that causes rotation around a longitudinal axis, Distance of Node From Rotor A is the length of the line segment from a node to the axis of rotation of Rotor A in a torsional system & Mass Moment of Inertia of Rotor A is a measure of the rotor's resistance to changes in its rotation rate, influencing torsional vibration behavior.

How to calculate Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System?

Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System formula is defined as the rate at which the rotor A of a two-rotor system vibrates freely when twisted and then released, measuring the system's natural tendency to oscillate at a specific frequency is calculated using Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia)/(Distance of Node From Rotor A*Mass Moment of Inertia of Rotor A)))/(2*pi). To calculate Natural Frequency of Free Torsional Vibration for Rotor A of Two Rotor System, you need Modulus of Rigidity (G), Polar Moment of Inertia (J), Distance of Node From Rotor A (l_A) & Mass Moment of Inertia of Rotor A (I_A'). With our tool, you need to enter the respective value for Modulus of Rigidity, Polar Moment of Inertia, Distance of Node From Rotor A & Mass Moment of Inertia of Rotor A 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 A & Mass Moment of Inertia of Rotor A. 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 B*Mass Moment of Inertia of Rotor B)))/(2*pi)

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