Natural Frequency of Vibration Calculator

✖torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.ⓘ Torsional Stiffness [q]			+10% -10%
✖Mass moment of inertia of disc is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.ⓘ Mass Moment of Inertia of Disc [I_disc]			+10% -10%

✖Frequency is the number of times something happens in a particular period.ⓘ Natural Frequency of Vibration [f]

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Formula

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Natural Frequency of Vibration

Formula

`"f" = (sqrt("q"/"I"_{"disc"}))/(2*pi)`

Example

`"0.148532Hz"=(sqrt("5.4N/m"/"6.2kg·m²"))/(2*pi)`

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Natural Frequency of Vibration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Frequency = (sqrt(Torsional Stiffness/Mass Moment of Inertia of Disc))/(2*pi)
f = (sqrt(q/I_disc))/(2*pi)
This formula uses 1 Constants, 1 Functions, 3 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.
Torsional Stiffness - (Measured in Newton per Meter) - torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.
Mass Moment of Inertia of Disc - (Measured in Kilogram Square Meter) - Mass moment of inertia of disc 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

Torsional Stiffness: 5.4 Newton per Meter --> 5.4 Newton per Meter No Conversion Required
Mass Moment of Inertia of Disc: 6.2 Kilogram Square Meter --> 6.2 Kilogram Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = (sqrt(q/I_disc))/(2*pi) --> (sqrt(5.4/6.2))/(2*pi)

Evaluating ... ...

f = 0.148532389167479

STEP 3: Convert Result to Output's Unit

0.148532389167479 Hertz --> No Conversion Required

FINAL ANSWER

0.148532389167479 ≈ 0.148532 Hertz <-- Frequency

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Natural Frequency of Free Torsional Vibrations » Natural Frequency of Vibration

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National Institute Of Technology (NIT), Hamirpur

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< 13 Natural Frequency of Free Torsional Vibrations Calculators

Natural Frequency of Vibration

Go Frequency = (sqrt(Torsional Stiffness/Mass Moment of Inertia of Disc))/(2*pi)

Time Period for Vibrations

Go Time Period = 2*pi*sqrt(Mass Moment of Inertia of Disc/Torsional Stiffness)

Angular Velocity of Shaft

Go Angular Velocity = sqrt(Torsional Stiffness of Shaft/Mass Moment of Inertia of Disc)

Torsional Stiffness of Shaft given Time Period of Vibration

Go Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2

Moment of Inertia of Disc given Time Period of Vibration

Go Mass Moment of Inertia of Disc = (Time Period^2*Torsional Stiffness)/((2*pi)^2)

Moment of Inertia of Disc using Natural Frequency of Vibration

Go Mass Moment of Inertia of Disc = Torsional Stiffness/((2*pi*Frequency)^2)

Torsional Stiffness of Shaft given Natural Frequency of Vibration

Go Torsional Stiffness = (2*pi*Frequency)^2*Mass Moment of Inertia of Disc

Moment of Inertia of Disc given Angular Velocity

Go Mass Moment of Inertia of Disc = Torsional Stiffness of Shaft/(Angular Velocity^2)

Torsional Stiffness of Shaft given Angular Velocity

Go Torsional Stiffness of Shaft = Angular Velocity^2*Mass Moment of Inertia of Disc

Angular Displacement of Shaft from Mean Position

Go Angular Displacement of Shaft = Restoring Force/Torsional Stiffness

Restoring Force for Free Torsional Vibrations

Go Restoring Force = Torsional Stiffness*Angular Displacement of Shaft

Torsional Stiffness of Shaft

Go Torsional Stiffness = Restoring Force/Angular Displacement of Shaft

Accelerating Force

Go Force = Mass Moment of Inertia of Disc*Angular Acceleration

Natural Frequency of Vibration Formula

Frequency = (sqrt(Torsional Stiffness/Mass Moment of Inertia of Disc))/(2*pi)
f = (sqrt(q/I_disc))/(2*pi)

What causes torsional vibration?

Torsional vibrations are an example of machinery vibrations and are caused by the superposition of angular oscillations along the whole propulsion shaft system including propeller shaft, engine crankshaft, engine, gearbox, flexible coupling and along the intermediate shafts.

How to Calculate Natural Frequency of Vibration?

Natural Frequency of Vibration calculator uses Frequency = (sqrt(Torsional Stiffness/Mass Moment of Inertia of Disc))/(2*pi) to calculate the Frequency, The Natural frequency of vibration 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 Vibration using this online calculator? To use this online calculator for Natural Frequency of Vibration, enter Torsional Stiffness (q) & Mass Moment of Inertia of Disc (I_disc) and hit the calculate button. Here is how the Natural Frequency of Vibration calculation can be explained with given input values -> 1.849213 = (sqrt(5.4/6.2))/(2*pi).

FAQ

What is Natural Frequency of Vibration?

The Natural frequency of vibration 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(q/I_disc))/(2*pi) or Frequency = (sqrt(Torsional Stiffness/Mass Moment of Inertia of Disc))/(2*pi). torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque & Mass moment of inertia of disc is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis.

How to calculate Natural Frequency of Vibration?

The Natural frequency of vibration 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(Torsional Stiffness/Mass Moment of Inertia of Disc))/(2*pi). To calculate Natural Frequency of Vibration, you need Torsional Stiffness (q) & Mass Moment of Inertia of Disc (I_disc). With our tool, you need to enter the respective value for Torsional Stiffness & Mass Moment of Inertia of Disc 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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