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Length of Shaft given Natural Frequency Formula

GoLength of Shaft given Static Deflection Formula

GoLength of Shaft given Circular Frequency Formula

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Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft. Check FAQs

L shaft = {(\frac{π^{2}}{4 \cdot f^{2}} \cdot \frac{E \cdot I shaft \cdot g}{w})}^{\frac{1}{4}}

L_shaft - Length of Shaft?f - Frequency?E - Young's Modulus?I_shaft - Moment of inertia of shaft?g - Acceleration due to Gravity?w - Load per unit length?π - Archimedes' constant?

Length of Shaft given Natural Frequency Example

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Here is how the Length of Shaft given Natural Frequency equation looks like with Values.

Here is how the Length of Shaft given Natural Frequency equation looks like with Units.

Here is how the Length of Shaft given Natural Frequency equation looks like.

0.3568 = {(\frac{{3.1416}^{2}}{4 \cdot 90^{2}} \cdot \frac{15 \cdot 1.0855 \cdot 9.8}{3})}^{\frac{1}{4}}

0.3568m = {(\frac{{3.1416}^{2}}{4 \cdot {90Hz}^{2}} \cdot \frac{15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{3})}^{\frac{1}{4}}

0.3568 = {(\frac{{3.1416}^{2}}{4 \cdot 90^{2}} \cdot \frac{15 \cdot 1.0855 \cdot 9.8}{3})}^{\frac{1}{4}}

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Length of Shaft given Natural Frequency Solution

Follow our step by step solution on how to calculate Length of Shaft given Natural Frequency?

FIRST Step Consider the formula

L shaft = {(\frac{π^{2}}{4 \cdot f^{2}} \cdot \frac{E \cdot I shaft \cdot g}{w})}^{\frac{1}{4}}

Next Step Substitute values of Variables

∴

L shaft = {(\frac{π^{2}}{4 \cdot {90Hz}^{2}} \cdot \frac{15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{3})}^{\frac{1}{4}}

Next Step Substitute values of Constants

∴

L shaft = {(\frac{{3.1416}^{2}}{4 \cdot {90Hz}^{2}} \cdot \frac{15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{3})}^{\frac{1}{4}}

Next Step Prepare to Evaluate

∴

L shaft = {(\frac{{3.1416}^{2}}{4 \cdot 90^{2}} \cdot \frac{15 \cdot 1.0855 \cdot 9.8}{3})}^{\frac{1}{4}}

Next Step Evaluate

∴

L shaft = 0.356777420485813m

LAST Step Rounding Answer

∴

L shaft = 0.3568m

Length of Shaft given Natural Frequency Formula Elements

Variables

Constants

Length of Shaft

Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.

Symbol: L_shaft

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Shaft

Frequency

Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior.

Symbol: f

Measurement: FrequencyUnit: Hz

Note: Value can be positive or negative.

Formulas to find Frequency

Young's Modulus

Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.

Symbol: E

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Moment of inertia of shaft

Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.

Symbol: I_shaft

Measurement: Moment of InertiaUnit: kg·m²

Note: Value should be greater than 0.

Formulas to find Moment of inertia of shaft

Acceleration due to Gravity

Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, affecting natural frequency of free transverse vibrations.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value should be greater than 0.

Formulas to find Acceleration due to Gravity

Load per unit length

Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.

Symbol: w

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Load per unit length

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 Length of Shaft

Go Length of Shaft given Static Deflection

L shaft = {(\frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot w})}^{\frac{1}{4}}

Go Length of Shaft given Circular Frequency

L shaft = {(\frac{π^{4}}{{ω n}^{2}} \cdot \frac{E \cdot I shaft \cdot g}{w})}^{\frac{1}{4}}

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

Go Circular Frequency given Static Deflection

ω n = 2 \cdot π \cdot \frac{0.5615}{\sqrt{δ}}

Go Natural Frequency given Static Deflection

f = \frac{0.5615}{\sqrt{δ}}

Go Uniformly Distributed Load Unit Length given Static Deflection

w = \frac{δ \cdot 384 \cdot E \cdot I shaft}{5 \cdot {L shaft}^{4}}

Go Moment of Inertia of Shaft given Static Deflection given Load per Unit Length

I shaft = \frac{5 \cdot w \cdot {L shaft}^{4}}{384 \cdot E \cdot δ}

How to Evaluate Length of Shaft given Natural Frequency?

Length of Shaft given Natural Frequency evaluator uses Length of Shaft = ((pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4) to evaluate the Length of Shaft, Length of Shaft given Natural Frequency formula is defined as a measure of the length of a shaft in a mechanical system, which is influenced by the natural frequency of free transverse vibrations, modulus of elasticity, moment of inertia, and weight per unit length of the shaft. Length of Shaft is denoted by L_shaft symbol.

How to evaluate Length of Shaft given Natural Frequency using this online evaluator? To use this online evaluator for Length of Shaft given Natural Frequency, enter Frequency (f), Young's Modulus (E), Moment of inertia of shaft (I_shaft), Acceleration due to Gravity (g) & Load per unit length (w) and hit the calculate button.

FAQs on Length of Shaft given Natural Frequency

What is the formula to find Length of Shaft given Natural Frequency?

The formula of Length of Shaft given Natural Frequency is expressed as Length of Shaft = ((pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4). Here is an example- 0.356777 = ((pi^2)/(4*90^2)*(15*1.085522*9.8)/(3))^(1/4).

How to calculate Length of Shaft given Natural Frequency?

With Frequency (f), Young's Modulus (E), Moment of inertia of shaft (I_shaft), Acceleration due to Gravity (g) & Load per unit length (w) we can find Length of Shaft given Natural Frequency using the formula - Length of Shaft = ((pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4). This formula also uses Archimedes' constant .

What are the other ways to Calculate Length of Shaft?

Here are the different ways to Calculate Length of Shaft-

Length of Shaft=((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)
Length of Shaft=((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)

Can the Length of Shaft given Natural Frequency be negative?

No, the Length of Shaft given Natural Frequency, measured in Length cannot be negative.

Which unit is used to measure Length of Shaft given Natural Frequency?

Length of Shaft given Natural Frequency is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Length of Shaft given Natural Frequency can be measured.

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Length of Shaft given Natural Frequency Formula

​GoLength of Shaft given Static Deflection Formula

​GoLength of Shaft given Circular Frequency Formula

Length of Shaft given Natural Frequency Example

Length of Shaft given Natural Frequency Solution

Length of Shaft given Natural Frequency Formula Elements

Other Formulas to find Length of Shaft

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

How to Evaluate Length of Shaft given Natural Frequency?

FAQs on Length of Shaft given Natural Frequency

Variable Name

GoLength of Shaft given Static Deflection Formula

GoLength of Shaft given Circular Frequency Formula