Natural Frequency given Static Deflection Calculator

✖Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.ⓘ Natural Frequency given Static Deflection [f]

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Formula

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Natural Frequency given Static Deflection

Formula

`"f" = 0.5615/(sqrt("δ"))`

Example

`"2.092587Hz"=0.5615/(sqrt("0.072m"))`

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Natural Frequency given Static Deflection Solution

STEP 0: Pre-Calculation Summary

Formula Used

Frequency = 0.5615/(sqrt(Static Deflection))
f = 0.5615/(sqrt(δ))
This formula uses 1 Functions, 2 Variables

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

Frequency - (Measured in Hertz) - Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.
Static Deflection - (Measured in Meter) - Static deflection is the extension or compression of the constraint.

STEP 1: Convert Input(s) to Base Unit

Static Deflection: 0.072 Meter --> 0.072 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f = 0.5615/(sqrt(δ)) --> 0.5615/(sqrt(0.072))

Evaluating ... ...

f = 2.09258694894355

STEP 3: Convert Result to Output's Unit

2.09258694894355 Hertz --> No Conversion Required

FINAL ANSWER

2.09258694894355 ≈ 2.092587 Hertz <-- 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 » Natural Frequency given Static Deflection

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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

Natural Frequency given Static Deflection Formula

Frequency = 0.5615/(sqrt(Static Deflection))
f = 0.5615/(sqrt(δ))

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 Natural Frequency given Static Deflection?

Natural Frequency given Static Deflection calculator uses Frequency = 0.5615/(sqrt(Static Deflection)) to calculate the Frequency, The Natural Frequency given Static Deflection formula is defined as set of frequencies at which they naturally vibrate. Frequency is denoted by f symbol.

How to calculate Natural Frequency given Static Deflection using this online calculator? To use this online calculator for Natural Frequency given Static Deflection, enter Static Deflection (δ) and hit the calculate button. Here is how the Natural Frequency given Static Deflection calculation can be explained with given input values -> 2.092587 = 0.5615/(sqrt(0.072)).

FAQ

What is Natural Frequency given Static Deflection?

The Natural Frequency given Static Deflection formula is defined as set of frequencies at which they naturally vibrate and is represented as f = 0.5615/(sqrt(δ)) or Frequency = 0.5615/(sqrt(Static Deflection)). Static deflection is the extension or compression of the constraint.

How to calculate Natural Frequency given Static Deflection?

The Natural Frequency given Static Deflection formula is defined as set of frequencies at which they naturally vibrate is calculated using Frequency = 0.5615/(sqrt(Static Deflection)). To calculate Natural Frequency given Static Deflection, you need Static Deflection (δ). With our tool, you need to enter the respective value for Static Deflection 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 Frequency?

In this formula, Frequency uses Static Deflection. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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