Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations 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%
✖Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.ⓘ Mass Moment of Inertia of Disc [I_d]			+10% -10%
✖Total Mass Moment of Inertia is the rotational inertia of an object determined by its mass distribution and shape in a torsional vibration system.ⓘ Total Mass Moment of Inertia [I_c]			+10% -10%

✖torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.ⓘ Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations [q]

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Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations Solution

STEP 0: Pre-Calculation Summary

Formula Used

Torsional Stiffness = (2*pi*Frequency)^2*(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)
q = (2*pi*f)^2*(I_d+I_c/3)
This formula uses 1 Constants, 4 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.
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.
Mass Moment of Inertia of Disc - (Measured in Kilogram Square Meter) - Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis.
Total Mass Moment of Inertia - (Measured in Kilogram Square Meter) - Total Mass Moment of Inertia is the rotational inertia of an object determined by its mass distribution and shape in a torsional vibration system.

STEP 1: Convert Input(s) to Base Unit

Frequency: 0.12 Hertz --> 0.12 Hertz 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

q = (2*pi*f)^2*(I_d+I_c/3) --> (2*pi*0.12)^2*(6.2+10.65/3)

Evaluating ... ...

q = 5.54276983165178

STEP 3: Convert Result to Output's Unit

5.54276983165178 Newton per Meter --> No Conversion Required

FINAL ANSWER

5.54276983165178 ≈ 5.54277 Newton per Meter <-- Torsional Stiffness

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Torsional Vibrations » Mechanical » Effect of Inertia of Constraint on Torsional Vibrations » Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations

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< Effect of Inertia of Constraint on Torsional Vibrations Calculators

Kinetic Energy Possessed by Element

LaTeX 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)

Angular Velocity of Element

LaTeX Go Angular Velocity = (Angular Velocity of Free End*Distance Between Small Element and Fixed End)/Length of Constraint

Mass Moment of Inertia of Element

LaTeX Go Moment of Inertia = (Length of Small Element*Total Mass Moment of Inertia)/Length of Constraint

Total Kinetic Energy of Constraint

LaTeX Go Kinetic Energy = (Total Mass Moment of Inertia*Angular Velocity of Free End^2)/6

Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations Formula

LaTeX Go

Torsional Stiffness = (2*pi*Frequency)^2*(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3)
q = (2*pi*f)^2*(I_d+I_c/3)

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 Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations?

Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations calculator uses Torsional Stiffness = (2*pi*Frequency)^2*(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3) to calculate the Torsional Stiffness, Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations formula is defined as a measure of the shaft's resistance to twisting forces caused by the constraint, which affects the torsional vibrations of the shaft, providing a critical parameter in the design and analysis of mechanical systems. Torsional Stiffness is denoted by q symbol.

How to calculate Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations using this online calculator? To use this online calculator for Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations, enter Frequency (f), Mass Moment of Inertia of Disc (I_d) & Total Mass Moment of Inertia (I_c) and hit the calculate button. Here is how the Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations calculation can be explained with given input values -> 5.54277 = (2*pi*0.12)^2*(6.2+10.65/3).

FAQ

What is Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations?

Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations formula is defined as a measure of the shaft's resistance to twisting forces caused by the constraint, which affects the torsional vibrations of the shaft, providing a critical parameter in the design and analysis of mechanical systems and is represented as q = (2*pi*f)^2*(I_d+I_c/3) or Torsional Stiffness = (2*pi*Frequency)^2*(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3). 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, Mass Moment of Inertia of Disc is the rotational inertia of a disc that resists changes in its rotational motion, used in torsional vibration analysis & Total Mass Moment of Inertia is the rotational inertia of an object determined by its mass distribution and shape in a torsional vibration system.

How to calculate Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations?

Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations formula is defined as a measure of the shaft's resistance to twisting forces caused by the constraint, which affects the torsional vibrations of the shaft, providing a critical parameter in the design and analysis of mechanical systems is calculated using Torsional Stiffness = (2*pi*Frequency)^2*(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3). To calculate Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations, you need Frequency (f), Mass Moment of Inertia of Disc (I_d) & Total Mass Moment of Inertia (I_c). With our tool, you need to enter the respective value for Frequency, 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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