Natural Frequency of Torsional Vibration due to Effect of Inertia of Constraint Solution

STEP 0: Pre-Calculation Summary
Formula Used
Frequency = (sqrt(Torsional Stiffness/(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)))/(2*pi)
f = (sqrt(q/(Idisc+Ic/3)))/(2*pi)
This formula uses 1 Constants, 1 Functions, 4 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.
Total Mass Moment of Inertia - (Measured in Kilogram Square Meter) - Total Mass Moment of Inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analog to mass.
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
Total Mass Moment of Inertia: 10.65 Kilogram Square Meter --> 10.65 Kilogram Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
f = (sqrt(q/(Idisc+Ic/3)))/(2*pi) --> (sqrt(5.4/(6.2+10.65/3)))/(2*pi)
Evaluating ... ...
f = 0.118444446749783
STEP 3: Convert Result to Output's Unit
0.118444446749783 Hertz --> No Conversion Required
FINAL ANSWER
0.118444446749783 0.118444 Hertz <-- Frequency
(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur
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8 Effect of Inertia of Constraint on Torsional Vibrations Calculators

Kinetic Energy Possessed by Element
Go Kinetic Energy = (Total Mass Moment of Inertia*(Angular Velocity of Free End*Distance between Small Element and Fixed End)^2*Length of Small Element)/(2*Length of Constraint^3)
Natural Frequency of Torsional Vibration due to Effect of Inertia of Constraint
Go Frequency = (sqrt(Torsional Stiffness/(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)))/(2*pi)
Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations
Go Torsional Stiffness = (2*pi*Frequency)^2*(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)
Angular Velocity of Element
Go Angular Velocity = (Angular Velocity of Free End*Distance between Small Element and Fixed End)/Length of Constraint
Mass Moment of Inertia of Element
Go Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint
Angular Velocity of Free End using Kinetic Energy of Constraint
Go Angular Velocity of Free End = sqrt((6*Kinetic Energy)/Total Mass Moment of Inertia)
Total Mass Moment of Inertia of Constraint given Kinetic Energy of Constraint
Go Total Mass Moment of Inertia = (6*Kinetic Energy)/(Angular Velocity of Free End^2)
Total Kinetic Energy of Constraint
Go Kinetic Energy = (Total Mass Moment of Inertia*Angular Velocity of Free End^2)/6

Natural Frequency of Torsional Vibration due to Effect of Inertia of Constraint Formula

Frequency = (sqrt(Torsional Stiffness/(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)))/(2*pi)
f = (sqrt(q/(Idisc+Ic/3)))/(2*pi)

What causes torsional vibration on the shaft?

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 Torsional Vibration due to Effect of Inertia of Constraint?

Natural Frequency of Torsional Vibration due to Effect of Inertia of Constraint calculator uses Frequency = (sqrt(Torsional Stiffness/(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)))/(2*pi) to calculate the Frequency, The Natural frequency of torsional vibration due to effect of inertia of constraint 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 Torsional Vibration due to Effect of Inertia of Constraint using this online calculator? To use this online calculator for Natural Frequency of Torsional Vibration due to Effect of Inertia of Constraint, enter Torsional Stiffness (q), Mass Moment of Inertia of Disc (Idisc) & Total Mass Moment of Inertia (Ic) and hit the calculate button. Here is how the Natural Frequency of Torsional Vibration due to Effect of Inertia of Constraint calculation can be explained with given input values -> 0.118444 = (sqrt(5.4/(6.2+10.65/3)))/(2*pi).

FAQ

What is Natural Frequency of Torsional Vibration due to Effect of Inertia of Constraint?
The Natural frequency of torsional vibration due to effect of inertia of constraint 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/(Idisc+Ic/3)))/(2*pi) or Frequency = (sqrt(Torsional Stiffness/(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)))/(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 & Total Mass Moment of Inertia measures the extent to which an object resists rotational acceleration about an axis, and is the rotational analog to mass.
How to calculate Natural Frequency of Torsional Vibration due to Effect of Inertia of Constraint?
The Natural frequency of torsional vibration due to effect of inertia of constraint 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+Total Mass Moment of Inertia/3)))/(2*pi). To calculate Natural Frequency of Torsional Vibration due to Effect of Inertia of Constraint, you need Torsional Stiffness (q), Mass Moment of Inertia of Disc (Idisc) & Total Mass Moment of Inertia (Ic). With our tool, you need to enter the respective value for Torsional Stiffness, Mass Moment of Inertia of Disc & Total Mass Moment of Inertia 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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