FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

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

Fx Copy

LaTeX Copy

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. Check FAQs

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

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

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

With values

With units

Only example

Here is how the Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System equation looks like with Values.

Here is how the Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System equation looks like with Units.

Here is how the Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System equation looks like.

39.7942 = \frac{{(2 \cdot 3.1416 \cdot 0.12)}^{2} \cdot 7000 \cdot 100}{10}

39.7942N/m² = \frac{{(2 \cdot 3.1416 \cdot 0.12Hz)}^{2} \cdot 7000mm \cdot 100kg·m²}{10m⁴}

39.7942 = \frac{{(2 \cdot 3.1416 \cdot 0.12)}^{2} \cdot 7000 \cdot 100}{10}

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Theory of Machine » fx Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System

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

Follow our step by step solution on how to calculate Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

G = \frac{{(2 \cdot π \cdot 0.12Hz)}^{2} \cdot 7000mm \cdot 100kg·m²}{10m⁴}

Next Step Substitute values of Constants

∴

G = \frac{{(2 \cdot 3.1416 \cdot 0.12Hz)}^{2} \cdot 7000mm \cdot 100kg·m²}{10m⁴}

Next Step Convert Units

∴

G = \frac{{(2 \cdot 3.1416 \cdot 0.12Hz)}^{2} \cdot 7m \cdot 100kg·m²}{10m⁴}

Next Step Prepare to Evaluate

∴

G = \frac{{(2 \cdot 3.1416 \cdot 0.12)}^{2} \cdot 7 \cdot 100}{10}

Next Step Evaluate

∴

G = 39.7942449451923Pa

Next Step Convert to Output's Unit

∴

G = 39.7942449451923N/m²

LAST Step Rounding Answer

∴

G = 39.7942N/m²

Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System Formula Elements

Variables

Constants

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

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

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

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

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 Free Torsional Vibrations of Single Rotor System category

Go Natural Frequency of Free Torsional Vibration of Single Rotor System

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

How to Evaluate Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System evaluator uses Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft to evaluate the Modulus of Rigidity, Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System formula is defined as a measure of the shaft's stiffness in torsion, which is essential in determining the torsional vibration characteristics of a single rotor system, particularly in the context of mechanical engineering and rotor dynamics. Modulus of Rigidity is denoted by G symbol.

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

FAQs on Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System

What is the formula to find Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

The formula of Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System is expressed as Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft. Here is an example- 39.79424 = ((2*pi*0.12)^2*7*100)/10.

How to calculate Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

With Frequency (f), Length of Shaft (L), Moment of inertia of Shaft (I_s) & Polar Moment of Inertia of Shaft (J_s) we can find Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System using the formula - Modulus of Rigidity = ((2*pi*Frequency)^2*Length of Shaft*Moment of inertia of Shaft)/Polar Moment of Inertia of Shaft. This formula also uses Archimedes' constant .

Can the Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System be negative?

No, the Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System, measured in Pressure cannot be negative.

Which unit is used to measure Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System is usually measured using the Newton per Square Meter[N/m²] for Pressure. Pascal[N/m²], Kilopascal[N/m²], Bar[N/m²] are the few other units in which Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

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

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

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

Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System Formula Elements

Other formulas in Free Torsional Vibrations of Single Rotor System category

How to Evaluate Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System?

FAQs on Modulus of Rigidity of Shaft for Free Torsional Vibration of Single Rotor System

Variable Name