Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System Calculator

✖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.ⓘ Frequency [f]			+10% -10%
✖Length of Shaft is the distance from the axis of rotation to the point where the shaft is clamped or supported in a torsional vibration system.ⓘ Length of Shaft [L]			+10% -10%
✖Moment of inertia of Shaft is a measure of the shaft's resistance to torsional deformation, which affects the vibration characteristics of the system.ⓘ Moment of inertia of Shaft [I_s]			+10% -10%
✖Polar Moment of Inertia of Shaft is the resistance of a shaft to torsional deformation, depending on the shaft's geometry and mass distribution.ⓘ Polar Moment of Inertia of Shaft [J_s]			+10% -10%

✖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 of Shaft for Free Torsional Vibration of Single Rotor System [G]

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Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System Solution

STEP 0: Pre-Calculation Summary

Formula Used

Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft
G = ((2*pi*f)^2*L*I_s)/J_s
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.
Length of Shaft - (Measured in Meter) - Length of Shaft is the distance from the axis of rotation to the point where the shaft is clamped or supported in a torsional vibration system.
Moment of inertia of Shaft - (Measured in Kilogram Square Meter) - Moment of inertia of Shaft is a measure of the shaft's resistance to torsional deformation, which affects the vibration characteristics of the system.
Polar Moment of Inertia of Shaft - (Measured in Meter⁴) - Polar Moment of Inertia of Shaft is the resistance of a shaft to torsional deformation, depending on the shaft's geometry and mass distribution.

STEP 1: Convert Input(s) to Base Unit

Frequency: 0.12 Hertz --> 0.12 Hertz 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
Polar Moment of Inertia of Shaft: 10 Meter⁴ --> 10 Meter⁴ No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

G = ((2*pi*f)^2*L*I_s)/J_s --> ((2*pi*0.12)^2*7*100)/10

Evaluating ... ...

G = 39.7942449451923

STEP 3: Convert Result to Output's Unit

39.7942449451923 Pascal -->39.7942449451923 Newton per Square Meter (Check conversion here)

FINAL ANSWER

39.7942449451923 ≈ 39.79424 Newton per Square Meter <-- Modulus of Rigidity

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Free Torsional Vibrations of Rotor Systems » Mechanical » Free Torsional Vibrations of Single Rotor System » Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System

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< Free Torsional Vibrations of Single Rotor System Calculators

Natural Frequency of Free Torsional Vibration of Single Rotor System

LaTeX 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

LaTeX Go Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft

Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System Formula

LaTeX Go

Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft
G = ((2*pi*f)^2*L*I_s)/J_s

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 Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System calculator uses Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft to calculate the Modulus of Rigidity, Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System formula is defined as a measure of the shaft's stiffness in torsion, which is essential in determining the torsional vibration characteristics of a single rotor system, particularly in the context of mechanical engineering and rotor dynamics. Modulus of Rigidity is denoted by G symbol.

How to calculate Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System using this online calculator? To use this online calculator for Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System, enter Frequency (f), Length of Shaft (L), Moment of inertia of Shaft (I_s) & Polar Moment of Inertia of Shaft (J_s) and hit the calculate button. Here is how the Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System calculation can be explained with given input values -> 39.79424 = ((2*pi*0.12)^2*7*100)/10.

FAQ

What is Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System formula is defined as a measure of the shaft's stiffness in torsion, which is essential in determining the torsional vibration characteristics of a single rotor system, particularly in the context of mechanical engineering and rotor dynamics and is represented as G = ((2*pi*f)^2*L*I_s)/J_s or Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft. 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, Length of Shaft is the distance from the axis of rotation to the point where the shaft is clamped or supported in a torsional vibration system, Moment of inertia of Shaft is a measure of the shaft's resistance to torsional deformation, which affects the vibration characteristics of the system & Polar Moment of Inertia of Shaft is the resistance of a shaft to torsional deformation, depending on the shaft's geometry and mass distribution.

How to calculate Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System formula is defined as a measure of the shaft's stiffness in torsion, which is essential in determining the torsional vibration characteristics of a single rotor system, particularly in the context of mechanical engineering and rotor dynamics is calculated using Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft. To calculate Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System, you need Frequency (f), Length of Shaft (L), Moment of inertia of Shaft (I_s) & Polar Moment of Inertia of Shaft (J_s). With our tool, you need to enter the respective value for Frequency, Length of Shaft, Moment of inertia of Shaft & Polar 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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