Natural Frequency of Free Torsional Vibration of Single 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 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%
✖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%

✖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 of Single Rotor System [f]

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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*J_s)/(L*I_s)))/(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 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.
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.

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*J_s)/(L*I_s)))/(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 00.004 seconds)

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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

Natural Frequency of Free Torsional Vibration of Single Rotor System Formula

LaTeX Go

Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia of Shaft)/(Length of Shaft*Moment of inertia of Shaft)))/(2*pi)
f = (sqrt((G*J_s)/(L*I_s)))/(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, Natural Frequency of Free Torsional Vibration of Single Rotor System formula is defined as a measure of the frequency at which a single rotor system vibrates freely in a torsional mode, influenced by the shaft's stiffness, moment of inertia, and length, providing insights into the system's dynamic behavior. 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 (J_s), Length of Shaft (L) & Moment of inertia of Shaft (I_s) 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?

Natural Frequency of Free Torsional Vibration of Single Rotor System formula is defined as a measure of the frequency at which a single rotor system vibrates freely in a torsional mode, influenced by the shaft's stiffness, moment of inertia, and length, providing insights into the system's dynamic behavior and is represented as f = (sqrt((G*J_s)/(L*I_s)))/(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 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 of Shaft is the resistance of a shaft to torsional deformation, depending on the shaft's geometry and mass distribution, 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.

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

Natural Frequency of Free Torsional Vibration of Single Rotor System formula is defined as a measure of the frequency at which a single rotor system vibrates freely in a torsional mode, influenced by the shaft's stiffness, moment of inertia, and length, providing insights into the system's dynamic behavior 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 (J_s), Length of Shaft (L) & Moment of inertia of Shaft (I_s). 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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