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Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations 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)}^{2} \cdot (I d + \frac{I c}{3})

q - Torsional Stiffness?f - Frequency?I_d - Mass Moment of Inertia of Disc?I_c - Total Mass Moment of Inertia?π - Archimedes' constant?

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

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Here is how the Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations equation looks like with Values.

Here is how the Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations equation looks like with Units.

Here is how the Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations equation looks like.

5.5428 = {(2 \cdot 3.1416 \cdot 0.12)}^{2} \cdot (6.2 + \frac{10.65}{3})

5.5428N/m = {(2 \cdot 3.1416 \cdot 0.12Hz)}^{2} \cdot (6.2kg·m² + \frac{10.65kg·m²}{3})

5.5428 = {(2 \cdot 3.1416 \cdot 0.12)}^{2} \cdot (6.2 + \frac{10.65}{3})

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

Follow our step by step solution on how to calculate Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations?

FIRST Step Consider the formula

q = {(2 \cdot π \cdot f)}^{2} \cdot (I d + \frac{I c}{3})

Next Step Substitute values of Variables

∴

q = {(2 \cdot π \cdot 0.12Hz)}^{2} \cdot (6.2kg·m² + \frac{10.65kg·m²}{3})

Next Step Substitute values of Constants

∴

q = {(2 \cdot 3.1416 \cdot 0.12Hz)}^{2} \cdot (6.2kg·m² + \frac{10.65kg·m²}{3})

Next Step Prepare to Evaluate

∴

q = {(2 \cdot 3.1416 \cdot 0.12)}^{2} \cdot (6.2 + \frac{10.65}{3})

Next Step Evaluate

∴

q = 5.54276983165178N/m

LAST Step Rounding Answer

∴

q = 5.5428N/m

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

Frequency

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.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value should be greater than 0.

Formulas to find 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

Total Mass Moment of Inertia

Total Mass Moment of Inertia is the rotational inertia of an object determined by its mass distribution and shape in a torsional vibration system.

Symbol: I_c

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Total Mass Moment of Inertia

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 in Effect of Inertia of Constraint on Torsional Vibrations category

Go Mass Moment of Inertia of Element

I = \frac{δ x \cdot I c}{l}

Go Angular Velocity of Element

ω = \frac{ω f \cdot x}{l}

Go Kinetic Energy Possessed by Element

KE = \frac{I c \cdot {(ω f \cdot x)}^{2} \cdot δ x}{2 \cdot l^{3}}

Go Total Kinetic Energy of Constraint

KE = \frac{I c \cdot {ω f}^{2}}{6}

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

Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations evaluator uses Torsional Stiffness = (2*pi*Frequency)^2*(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3) to evaluate 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 evaluate Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations using this online evaluator? To use this online evaluator 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.

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

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

The formula of Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations is expressed as Torsional Stiffness = (2*pi*Frequency)^2*(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3). Here is an example- 5.54277 = (2*pi*0.12)^2*(6.2+10.65/3).

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

With Frequency (f), Mass Moment of Inertia of Disc (I_d) & Total Mass Moment of Inertia (I_c) we can find Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations using the formula - Torsional Stiffness = (2*pi*Frequency)^2*(Mass Moment of Inertia of Disc+Total Mass Moment of Inertia/3). This formula also uses Archimedes' constant .

Can the Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations be negative?

No, the Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations, measured in Stiffness Constant cannot be negative.

Which unit is used to measure Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations?

Torsional Stiffness of Shaft due to Effect of Constraint on Torsional Vibrations 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 due to Effect of Constraint on Torsional Vibrations can be measured.

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

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

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

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

Other formulas in Effect of Inertia of Constraint on Torsional Vibrations category

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

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

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