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Torsional Stiffness of Shaft given Natural Frequency of Vibration Formula

GoTorsional Stiffness of Shaft given Time Period of Vibration Formula

GoTorsional Stiffness of Shaft Formula

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torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque. Check FAQs

q = {(2 \cdot π \cdot f n)}^{2} \cdot I d

q - Torsional Stiffness?f_n - Natural Frequency?I_d - Mass Moment of Inertia of Disc?π - Archimedes' constant?

Torsional Stiffness of Shaft given Natural Frequency of Vibration Example

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Here is how the Torsional Stiffness of Shaft given Natural Frequency of Vibration equation looks like with Values.

Here is how the Torsional Stiffness of Shaft given Natural Frequency of Vibration equation looks like with Units.

Here is how the Torsional Stiffness of Shaft given Natural Frequency of Vibration equation looks like.

5.4 = {(2 \cdot 3.1416 \cdot 0.1485)}^{2} \cdot 6.2

5.4N/m = {(2 \cdot 3.1416 \cdot 0.1485Hz)}^{2} \cdot 6.2kg·m²

5.4 = {(2 \cdot 3.1416 \cdot 0.1485)}^{2} \cdot 6.2

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Torsional Stiffness of Shaft given Natural Frequency of Vibration Solution

Follow our step by step solution on how to calculate Torsional Stiffness of Shaft given Natural Frequency of Vibration?

FIRST Step Consider the formula

q = {(2 \cdot π \cdot f n)}^{2} \cdot I d

Next Step Substitute values of Variables

∴

q = {(2 \cdot π \cdot 0.1485Hz)}^{2} \cdot 6.2kg·m²

Next Step Substitute values of Constants

∴

q = {(2 \cdot 3.1416 \cdot 0.1485Hz)}^{2} \cdot 6.2kg·m²

Next Step Prepare to Evaluate

∴

q = {(2 \cdot 3.1416 \cdot 0.1485)}^{2} \cdot 6.2

Next Step Evaluate

∴

q = 5.39997170311952N/m

LAST Step Rounding Answer

∴

q = 5.4N/m

Torsional Stiffness of Shaft given Natural Frequency of Vibration Formula Elements

Variables

Constants

Torsional Stiffness

torsional stiffness is the ability of an object to resist twisting when acted upon by an external force, torque.

Symbol: q

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Torsional Stiffness

Natural Frequency

Natural Frequency is the number of oscillations or cycles per second in a torsional vibration system, characterizing its inherent oscillatory behavior.

Symbol: f_n

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find Natural Frequency

Mass Moment of Inertia of Disc

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.

Symbol: I_d

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Mass Moment of Inertia of Disc

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Torsional Stiffness

Go Torsional Stiffness of Shaft given Time Period of Vibration

q = \frac{{(2 \cdot π)}^{2} \cdot I d}{{(t p)}^{2}}

Go Torsional Stiffness of Shaft

q = \frac{F r}{θ}

Other formulas in Natural Frequency of Free Torsional Vibrations category

Go Moment of Inertia of Disc using Natural Frequency of Vibration

I d = \frac{q}{{(2 \cdot π \cdot f n)}^{2}}

Go Moment of Inertia of Disc given Time Period of Vibration

I d = \frac{{t p}^{2} \cdot q}{{(2 \cdot π)}^{2}}

Go Time Period for Vibrations

t p = 2 \cdot π \cdot \sqrt{\frac{I d}{q}}

Go Moment of Inertia of Disc given Angular Velocity

I d = \frac{q r}{ω^{2}}

How to Evaluate Torsional Stiffness of Shaft given Natural Frequency of Vibration?

Torsional Stiffness of Shaft given Natural Frequency of Vibration evaluator uses Torsional Stiffness = (2*pi*Natural Frequency)^2*Mass Moment of Inertia of Disc to evaluate the Torsional Stiffness, Torsional Stiffness of Shaft given Natural Frequency of Vibration formula is defined as a measure of the shaft's resistance to twisting forces, which is essential in determining the shaft's ability to withstand torsional vibrations and maintain its structural integrity. Torsional Stiffness is denoted by q symbol.

How to evaluate Torsional Stiffness of Shaft given Natural Frequency of Vibration using this online evaluator? To use this online evaluator for Torsional Stiffness of Shaft given Natural Frequency of Vibration, enter Natural Frequency (f_n) & Mass Moment of Inertia of Disc (I_d) and hit the calculate button.

FAQs on Torsional Stiffness of Shaft given Natural Frequency of Vibration

What is the formula to find Torsional Stiffness of Shaft given Natural Frequency of Vibration?

The formula of Torsional Stiffness of Shaft given Natural Frequency of Vibration is expressed as Torsional Stiffness = (2*pi*Natural Frequency)^2*Mass Moment of Inertia of Disc. Here is an example- 5.399972 = (2*pi*0.148532)^2*6.2.

How to calculate Torsional Stiffness of Shaft given Natural Frequency of Vibration?

With Natural Frequency (f_n) & Mass Moment of Inertia of Disc (I_d) we can find Torsional Stiffness of Shaft given Natural Frequency of Vibration using the formula - Torsional Stiffness = (2*pi*Natural Frequency)^2*Mass Moment of Inertia of Disc. This formula also uses Archimedes' constant .

What are the other ways to Calculate Torsional Stiffness?

Here are the different ways to Calculate Torsional Stiffness-

Torsional Stiffness=((2*pi)^2*Mass Moment of Inertia of Disc)/(Time Period)^2
Torsional Stiffness=Restoring Force/Angular Displacement of Shaft

Can the Torsional Stiffness of Shaft given Natural Frequency of Vibration be negative?

No, the Torsional Stiffness of Shaft given Natural Frequency of Vibration, measured in Stiffness Constant cannot be negative.

Which unit is used to measure Torsional Stiffness of Shaft given Natural Frequency of Vibration?

Torsional Stiffness of Shaft given Natural Frequency of Vibration is usually measured using the Newton per Meter[N/m] for Stiffness Constant. Newton per Millimeter[N/m], Kilonewton per Millimeter[N/m] are the few other units in which Torsional Stiffness of Shaft given Natural Frequency of Vibration can be measured.

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Torsional Stiffness of Shaft given Natural Frequency of Vibration Formula

​GoTorsional Stiffness of Shaft given Time Period of Vibration Formula

​GoTorsional Stiffness of Shaft Formula

Torsional Stiffness of Shaft given Natural Frequency of Vibration Example

Torsional Stiffness of Shaft given Natural Frequency of Vibration Solution

Torsional Stiffness of Shaft given Natural Frequency of Vibration Formula Elements

Other Formulas to find Torsional Stiffness

Other formulas in Natural Frequency of Free Torsional Vibrations category

How to Evaluate Torsional Stiffness of Shaft given Natural Frequency of Vibration?

FAQs on Torsional Stiffness of Shaft given Natural Frequency of Vibration

Variable Name

GoTorsional Stiffness of Shaft given Time Period of Vibration Formula

GoTorsional Stiffness of Shaft Formula