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Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load Formula

GoCircular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Formula

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Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force. Check FAQs

ω n = \sqrt{\frac{504 \cdot E \cdot I shaft \cdot g}{w \cdot {L shaft}^{4}}}

ω_n - Natural Circular Frequency?E - Young's Modulus?I_shaft - Moment of inertia of shaft?g - Acceleration due to Gravity?w - Load per unit length?L_shaft - Length of Shaft?

Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load Example

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Here is how the Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load equation looks like with Values.

Here is how the Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load equation looks like with Units.

Here is how the Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load equation looks like.

13.3658 = \sqrt{\frac{504 \cdot 15 \cdot 1.0855 \cdot 9.8}{3 \cdot {3.5}^{4}}}

13.3658rad/s = \sqrt{\frac{504 \cdot 15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{3 \cdot {3.5m}^{4}}}

13.3658 = \sqrt{\frac{504 \cdot 15 \cdot 1.0855 \cdot 9.8}{3 \cdot {3.5}^{4}}}

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Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load Solution

Follow our step by step solution on how to calculate Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load?

FIRST Step Consider the formula

ω n = \sqrt{\frac{504 \cdot E \cdot I shaft \cdot g}{w \cdot {L shaft}^{4}}}

Next Step Substitute values of Variables

∴

ω n = \sqrt{\frac{504 \cdot 15N/m \cdot 1.0855kg·m² \cdot 9.8m/s²}{3 \cdot {3.5m}^{4}}}

Next Step Prepare to Evaluate

∴

ω n = \sqrt{\frac{504 \cdot 15 \cdot 1.0855 \cdot 9.8}{3 \cdot {3.5}^{4}}}

Next Step Evaluate

∴

ω n = 13.3658485060139rad/s

LAST Step Rounding Answer

∴

ω n = 13.3658rad/s

Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load Formula Elements

Variables

Functions

Natural Circular Frequency

Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force.

Symbol: ω_n

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Natural Circular 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

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

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 to find Natural Circular Frequency

Go Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

ω n = \frac{2 \cdot π \cdot 0.571}{\sqrt{δ}}

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

Go Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

δ = {(\frac{0.571}{f})}^{2}

Go Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

f = \frac{0.571}{\sqrt{δ}}

Go M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load

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

Go Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)

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

How to Evaluate Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load?

Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load evaluator uses Natural Circular Frequency = sqrt((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)) to evaluate the Natural Circular Frequency, Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load formula is defined as the rate at which a shaft fixed at both ends and carrying a uniformly distributed load vibrates naturally when it is subjected to free transverse vibrations, providing insight into the shaft's dynamic behavior. Natural Circular Frequency is denoted by ω_n symbol.

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

FAQs on Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load

What is the formula to find Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load?

The formula of Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load is expressed as Natural Circular Frequency = sqrt((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)). Here is an example- 13.36585 = sqrt((504*15*1.085522*9.8)/(3*3.5^4)).

How to calculate Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load?

With Young's Modulus (E), Moment of inertia of shaft (I_shaft), Acceleration due to Gravity (g), Load per unit length (w) & Length of Shaft (L_shaft) we can find Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load using the formula - Natural Circular Frequency = sqrt((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Natural Circular Frequency?

Here are the different ways to Calculate Natural Circular Frequency-

Natural Circular Frequency=(2*pi*0.571)/(sqrt(Static Deflection))

Can the Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load be negative?

No, the Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load, measured in Angular Velocity cannot be negative.

Which unit is used to measure Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load?

Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load is usually measured using the Radian per Second[rad/s] for Angular Velocity. Radian per Day[rad/s], Radian per Hour[rad/s], Radian per Minute[rad/s] are the few other units in which Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load can be measured.

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Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load Formula

​GoCircular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Formula

Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load Example

Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load Solution

Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load Formula Elements

Other Formulas to find Natural Circular Frequency

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

How to Evaluate Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load?

FAQs on Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load

Variable Name

GoCircular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) Formula