Torsional Stiffness of Shaft given Time Period of Vibration Solution

STEP 0: Pre-Calculation Summary
Formula Used
Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2
q = ((2*pi)^2*Idisc)/(tp)^2
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
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.
Time Period - (Measured in Second) - Time Period is the time taken by a complete cycle of the wave to pass a point.
STEP 1: Convert Input(s) to Base Unit
Mass Moment of Inertia of Disc: 6.2 Kilogram Square Meter --> 6.2 Kilogram Square Meter No Conversion Required
Time Period: 3 Second --> 3 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
q = ((2*pi)^2*Idisc)/(tp)^2 --> ((2*pi)^2*6.2)/(3)^2
Evaluating ... ...
q = 27.1962432385573
STEP 3: Convert Result to Output's Unit
27.1962432385573 Newton per Meter --> No Conversion Required
FINAL ANSWER
27.1962432385573 27.19624 Newton per Meter <-- Torsional Stiffness
(Calculation completed in 00.004 seconds)

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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

Torsional Stiffness of Shaft given Time Period of Vibration Formula

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

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 Torsional Stiffness of Shaft given Time Period of Vibration?

Torsional Stiffness of Shaft given Time Period of Vibration calculator uses Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2 to calculate the Torsional Stiffness, The Torsional Stiffness of Shaft given Time Period of Vibration formula is defined as the torque required for unit twist. Torsional Stiffness is denoted by q symbol.

How to calculate Torsional Stiffness of Shaft given Time Period of Vibration using this online calculator? To use this online calculator for Torsional Stiffness of Shaft given Time Period of Vibration, enter Mass Moment of Inertia of Disc (Idisc) & Time Period (tp) and hit the calculate button. Here is how the Torsional Stiffness of Shaft given Time Period of Vibration calculation can be explained with given input values -> 0.17546 = ((2*pi)^2*6.2)/(3)^2.

FAQ

What is Torsional Stiffness of Shaft given Time Period of Vibration?
The Torsional Stiffness of Shaft given Time Period of Vibration formula is defined as the torque required for unit twist and is represented as q = ((2*pi)^2*Idisc)/(tp)^2 or Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2. Mass moment of inertia of disc is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis & Time Period is the time taken by a complete cycle of the wave to pass a point.
How to calculate Torsional Stiffness of Shaft given Time Period of Vibration?
The Torsional Stiffness of Shaft given Time Period of Vibration formula is defined as the torque required for unit twist is calculated using Torsional Stiffness = ((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2. To calculate Torsional Stiffness of Shaft given Time Period of Vibration, you need Mass Moment of Inertia of Disc (Idisc) & Time Period (tp). With our tool, you need to enter the respective value for Mass Moment of Inertia of Disc & Time Period 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 Torsional Stiffness?
In this formula, Torsional Stiffness uses Mass Moment of Inertia of Disc & Time Period. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Torsional Stiffness = (2*pi*Frequency)^2*Mass Moment of Inertia of Disc
  • Torsional Stiffness = Restoring Force/Angular Displacement of Shaft
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