Circular Frequency due to Uniformly Distributed Load Calculator

✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%
✖Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.ⓘ Moment of inertia of shaft [I_shaft]			+10% -10%
✖Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Load per unit length is the distributed load which is spread over a surface or line.ⓘ Load per unit length [w]			+10% -10%
✖Length of shaft is the distance between two ends of shaft.ⓘ Length of Shaft [L_shaft]			+10% -10%

✖Natural Circular Frequency is a scalar measure of rotation rate.ⓘ Circular Frequency due to Uniformly Distributed Load [ω_n]

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Circular Frequency due to Uniformly Distributed Load

Formula

`"ω"_{"n"} = pi^2*sqrt(("E"*"I"_{"shaft"}*"g")/("w"*"L"_{"shaft"}^4))`

Example

`"8.356961rad/s"=pi^2*sqrt(("15N/m"*"6kg·m²"*"9.8m/s²")/("3"*("4500mm")^4))`

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Download Longitudinal and Transverse Vibrations Formula PDF

Circular Frequency due to Uniformly Distributed Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Natural Circular Frequency = pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
ω_n = pi^2*sqrt((E*I_shaft*g)/(w*L_shaft^4))
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sqrt(Number)

Variables Used

Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is a scalar measure of rotation rate.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Moment of inertia of shaft - (Measured in Kilogram Square Meter) - Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Load per unit length - Load per unit length is the distributed load which is spread over a surface or line.
Length of Shaft - (Measured in Meter) - Length of shaft is the distance between two ends of shaft.

STEP 1: Convert Input(s) to Base Unit

Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Moment of inertia of shaft: 6 Kilogram Square Meter --> 6 Kilogram Square Meter No Conversion Required
Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Load per unit length: 3 --> No Conversion Required
Length of Shaft: 4500 Millimeter --> 4.5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_n = pi^2*sqrt((E*I_shaft*g)/(w*L_shaft^4)) --> pi^2*sqrt((15*6*9.8)/(3*4.5^4))

Evaluating ... ...

ω_n = 8.35696114669495

STEP 3: Convert Result to Output's Unit

8.35696114669495 Radian per Second --> No Conversion Required

FINAL ANSWER

8.35696114669495 ≈ 8.356961 Radian per Second <-- Natural Circular Frequency

(Calculation completed in 00.020 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations Due to Uniformly Distributed Load Acting Over a Simply Supported Shaft » Circular Frequency due to Uniformly Distributed Load

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Indian Institute of Information Technology (IIIT), Guwahati

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< 17 Natural Frequency of Free Transverse Vibrations Due to Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Static Deflection at Distance x from End A

Go Static deflection at distance x from end A = (Load per unit length*(Distance of small section of shaft from end A^4-2*Length of Shaft*Distance of small section of shaft from end A+Length of Shaft^3*Distance of small section of shaft from end A))/(24*Young's Modulus*Moment of inertia of shaft)

Natural Frequency due to Uniformly Distributed Load

Go Frequency = pi/2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))

Circular Frequency due to Uniformly Distributed Load

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

Maximum Bending Moment at Distance x from End A

Go Bending Moment = (Load per unit length*Distance of small section of shaft from end A^2)/2-(Load per unit length*Length of Shaft*Distance of small section of shaft from end A)/2

Length of Shaft given Circular Frequency

Go 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)

Uniformly Distributed Load Unit Length given Circular Frequency

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

Moment of Inertia of Shaft given Circular Frequency

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

Length of Shaft given Natural Frequency

Go 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)

Uniformly Distributed Load Unit Length given Natural Frequency

Go Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)

Moment of Inertia of Shaft given Natural Frequency

Go Moment of inertia of shaft = (4*Frequency^2*Load per unit length*Length of Shaft^4)/(pi^2*Young's Modulus*Acceleration due to Gravity)

Length of Shaft given Static Deflection

Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)

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

Go Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)

Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load

Go Static Deflection = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)

Uniformly Distributed Load Unit Length given Static Deflection

Go Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4)

Circular Frequency given Static Deflection

Go Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))

Natural Frequency given Static Deflection

Go Frequency = 0.5615/(sqrt(Static Deflection))

Static Deflection using Natural Frequency

Go Static Deflection = (0.5615/Frequency)^2

Circular Frequency due to Uniformly Distributed Load Formula

Natural Circular Frequency = pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
ω_n = pi^2*sqrt((E*I_shaft*g)/(w*L_shaft^4))

What is transverse and longitudinal vibration?

The difference between transverse and longitudinal waves is the direction in which the waves shake. If the wave shakes perpendicular to the movement direction, it's a transverse wave, if it shakes in the movement direction, then it's a longitudinal wave.

How to Calculate Circular Frequency due to Uniformly Distributed Load?

Circular Frequency due to Uniformly Distributed Load calculator uses Natural Circular Frequency = pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)) to calculate the Natural Circular Frequency, The Circular frequency due to uniformly distributed load formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force. Natural Circular Frequency is denoted by ω_n symbol.

How to calculate Circular Frequency due to Uniformly Distributed Load using this online calculator? To use this online calculator for Circular Frequency due to 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. Here is how the Circular Frequency due to Uniformly Distributed Load calculation can be explained with given input values -> 8.356961 = pi^2*sqrt((15*6*9.8)/(3*4.5^4)).

FAQ

What is Circular Frequency due to Uniformly Distributed Load?

The Circular frequency due to uniformly distributed load formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force and is represented as ω_n = pi^2*sqrt((E*I_shaft*g)/(w*L_shaft^4)) or Natural Circular Frequency = pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)). Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation, Acceleration due to Gravity is acceleration gained by an object because of gravitational force, Load per unit length is the distributed load which is spread over a surface or line & Length of shaft is the distance between two ends of shaft.

How to calculate Circular Frequency due to Uniformly Distributed Load?

The Circular frequency due to uniformly distributed load formula is defined as the frequency at which a system tends to oscillate in the absence of any driving or damping force is calculated using Natural Circular Frequency = pi^2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)). To calculate Circular Frequency due to Uniformly Distributed Load, you need 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). With our tool, you need to enter the respective value for Young's Modulus, Moment of inertia of shaft, Acceleration due to Gravity, Load per unit length & Length of Shaft and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Natural Circular Frequency?

In this formula, Natural Circular Frequency uses Young's Modulus, Moment of inertia of shaft, Acceleration due to Gravity, Load per unit length & Length of Shaft. We can use 1 other way(s) to calculate the same, which is/are as follows -

Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))

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