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Natural Frequency of Free Torsional Vibration of Single Rotor System Formula

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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. Check FAQs

f = \frac{\sqrt{\frac{G \cdot J s}{L \cdot I s}}}{2 \cdot π}

f - Frequency?G - Modulus of Rigidity?J_s - Polar Moment of Inertia of Shaft?L - Length of Shaft?I_s - Moment of inertia of Shaft?π - Archimedes' constant?

Natural Frequency of Free Torsional Vibration of Single Rotor System Example

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Here is how the Natural Frequency of Free Torsional Vibration of Single Rotor System equation looks like with Values.

Here is how the Natural Frequency of Free Torsional Vibration of Single Rotor System equation looks like with Units.

Here is how the Natural Frequency of Free Torsional Vibration of Single Rotor System equation looks like.

0.1203 = \frac{\sqrt{\frac{40 \cdot 10}{7000 \cdot 100}}}{2 \cdot 3.1416}

0.1203Hz = \frac{\sqrt{\frac{40N/m² \cdot 10m⁴}{7000mm \cdot 100kg·m²}}}{2 \cdot 3.1416}

0.1203 = \frac{\sqrt{\frac{40 \cdot 10}{7000 \cdot 100}}}{2 \cdot 3.1416}

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Natural Frequency of Free Torsional Vibration of Single Rotor System Solution

Follow our step by step solution on how to calculate Natural Frequency of Free Torsional Vibration of Single Rotor System?

FIRST Step Consider the formula

f = \frac{\sqrt{\frac{G \cdot J s}{L \cdot I s}}}{2 \cdot π}

Next Step Substitute values of Variables

∴

f = \frac{\sqrt{\frac{40N/m² \cdot 10m⁴}{7000mm \cdot 100kg·m²}}}{2 \cdot π}

Next Step Substitute values of Constants

∴

f = \frac{\sqrt{\frac{40N/m² \cdot 10m⁴}{7000mm \cdot 100kg·m²}}}{2 \cdot 3.1416}

Next Step Convert Units

∴

f = \frac{\sqrt{\frac{40Pa \cdot 10m⁴}{7m \cdot 100kg·m²}}}{2 \cdot 3.1416}

Next Step Prepare to Evaluate

∴

f = \frac{\sqrt{\frac{40 \cdot 10}{7 \cdot 100}}}{2 \cdot 3.1416}

Next Step Evaluate

∴

f = 0.120309828385084Hz

LAST Step Rounding Answer

∴

f = 0.1203Hz

Natural Frequency of Free Torsional Vibration of Single Rotor System Formula Elements

Variables

Constants

Functions

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

Modulus of Rigidity

Modulus of Rigidity is the measure of the rigidity or stiffness of a material, which is a critical parameter in torsional vibration analysis of mechanical systems.

Symbol: G

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Modulus of Rigidity

Polar Moment of Inertia of Shaft

Polar Moment of Inertia of Shaft is the resistance of a shaft to torsional deformation, depending on the shaft's geometry and mass distribution.

Symbol: J_s

Measurement: Second Moment of AreaUnit: m⁴

Note: Value can be positive or negative.

Formulas to find Polar Moment of Inertia of Shaft

Length of Shaft

Length of Shaft is the distance from the axis of rotation to the point where the shaft is clamped or supported in a torsional vibration system.

Symbol: L

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Moment of inertia of Shaft

Moment of inertia of Shaft is a measure of the shaft's resistance to torsional deformation, which affects the vibration characteristics of the system.

Symbol: I_s

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of inertia of Shaft

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

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.

Syntax: sqrt(Number)

Other formulas in Free Torsional Vibrations of Single Rotor System category

Go Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System

G = \frac{{(2 \cdot π \cdot f)}^{2} \cdot L \cdot I s}{J s}

How to Evaluate Natural Frequency of Free Torsional Vibration of Single Rotor System?

Natural Frequency of Free Torsional Vibration of Single Rotor System evaluator uses Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia of Shaft)/(Length of Shaft*Moment of inertia of Shaft)))/(2*pi) to evaluate the Frequency, Natural Frequency of Free Torsional Vibration of Single Rotor System formula is defined as a measure of the frequency at which a single rotor system vibrates freely in a torsional mode, influenced by the shaft's stiffness, moment of inertia, and length, providing insights into the system's dynamic behavior. Frequency is denoted by f symbol.

How to evaluate Natural Frequency of Free Torsional Vibration of Single Rotor System using this online evaluator? To use this online evaluator for Natural Frequency of Free Torsional Vibration of Single Rotor System, enter Modulus of Rigidity (G), Polar Moment of Inertia of Shaft (J_s), Length of Shaft (L) & Moment of inertia of Shaft (I_s) and hit the calculate button.

FAQs on Natural Frequency of Free Torsional Vibration of Single Rotor System

What is the formula to find Natural Frequency of Free Torsional Vibration of Single Rotor System?

The formula of Natural Frequency of Free Torsional Vibration of Single Rotor System is expressed as Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia of Shaft)/(Length of Shaft*Moment of inertia of Shaft)))/(2*pi). Here is an example- 0.12031 = (sqrt((40*10)/(7*100)))/(2*pi).

How to calculate Natural Frequency of Free Torsional Vibration of Single Rotor System?

With Modulus of Rigidity (G), Polar Moment of Inertia of Shaft (J_s), Length of Shaft (L) & Moment of inertia of Shaft (I_s) we can find Natural Frequency of Free Torsional Vibration of Single Rotor System using the formula - Frequency = (sqrt((Modulus of Rigidity*Polar Moment of Inertia of Shaft)/(Length of Shaft*Moment of inertia of Shaft)))/(2*pi). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Natural Frequency of Free Torsional Vibration of Single Rotor System be negative?

No, the Natural Frequency of Free Torsional Vibration of Single Rotor System, measured in Frequency cannot be negative.

Which unit is used to measure Natural Frequency of Free Torsional Vibration of Single Rotor System?

Natural Frequency of Free Torsional Vibration of Single Rotor System is usually measured using the Hertz[Hz] for Frequency. Petahertz[Hz], Terahertz[Hz], Gigahertz[Hz] are the few other units in which Natural Frequency of Free Torsional Vibration of Single Rotor System can be measured.

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Natural Frequency of Free Torsional Vibration of Single Rotor System Formula

Natural Frequency of Free Torsional Vibration of Single Rotor System Example

Natural Frequency of Free Torsional Vibration of Single Rotor System Solution

Natural Frequency of Free Torsional Vibration of Single Rotor System Formula Elements

Other formulas in Free Torsional Vibrations of Single Rotor System category

How to Evaluate Natural Frequency of Free Torsional Vibration of Single Rotor System?

FAQs on Natural Frequency of Free Torsional Vibration of Single Rotor System

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