Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) 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 (Shaft Fixed, Uniformly Distributed Load) [f]

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

Formula

`"f" = 0.571/(sqrt("δ"))`

Example

`"2.127991Hz"=0.571/(sqrt("0.072m"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Frequency = 0.571/(sqrt(Static Deflection))
f = 0.571/(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 = 0.571/(sqrt(δ)) --> 0.571/(sqrt(0.072))

Evaluating ... ...

f = 2.1279913585873

STEP 3: Convert Result to Output's Unit

2.1279913585873 Hertz --> No Conversion Required

FINAL ANSWER

2.1279913585873 ≈ 2.127991 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 of a Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load » Natural Frequency given Static Deflection (Shaft Fixed, 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 of a Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Calculators

Static Deflection at Distance x from End A given Length of Shaft

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

Bending Moment at Some Distance from One End

Go Bending Moment = ((Load per unit length*Length of Shaft^2)/12)+((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)

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

Go 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))

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

Go Frequency = 3.573*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

Go Length of Shaft = ((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Natural Circular Frequency^2))^(1/4)

Load given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

Go Load per unit length = ((504*Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4*Natural Circular Frequency^2))

M.I of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

Go Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*Length of Shaft^4)/(504*Young's Modulus*Acceleration due to Gravity)

Length of Shaft given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)

Go Length of Shaft = 3.573^2*((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Frequency^2))^(1/4)

Load given Natural Frequency for Fixed Shaft and Uniformly Distributed Load

Go Load per unit length = (3.573^2)*((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4*Frequency^2))

M.I of Shaft given Natural Frequency for Fixed Shaft and Uniformly Distributed Load

Go Moment of inertia of shaft = (Frequency^2*Load per unit length*Length of Shaft^4)/(3.573^2*Young's Modulus*Acceleration due to Gravity)

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

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

Load using Static Deflection (Shaft Fixed, Uniformly Distributed Load)

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

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

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

Static Deflection of Shaft due to Uniformly Distributed Load given Length of Shaft

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

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

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

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

Go Frequency = 0.571/(sqrt(Static Deflection))

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

Go Static Deflection = (0.571/Frequency)^2

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

Frequency = 0.571/(sqrt(Static Deflection))
f = 0.571/(sqrt(δ))

What is a transverse wave definition?

Transverse wave, motion in which all points on a wave oscillate along paths at right angles to the direction of the wave's advance. Surface ripples on water, seismic S (secondary) waves, and electromagnetic (e.g., radio and light) waves are examples of transverse waves.

How to Calculate Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) calculator uses Frequency = 0.571/(sqrt(Static Deflection)) to calculate the Frequency, The Natural frequency given static deflection (Shaft fixed, uniformly distributed load) formula is defined as set of frequencies at which shaft naturally vibrate. Frequency is denoted by f symbol.

How to calculate Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) using this online calculator? To use this online calculator for Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load), enter Static Deflection (δ) and hit the calculate button. Here is how the Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) calculation can be explained with given input values -> 2.127991 = 0.571/(sqrt(0.072)).

FAQ

What is Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

The Natural frequency given static deflection (Shaft fixed, uniformly distributed load) formula is defined as set of frequencies at which shaft naturally vibrate and is represented as f = 0.571/(sqrt(δ)) or Frequency = 0.571/(sqrt(Static Deflection)). Static deflection is the extension or compression of the constraint.

How to calculate Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

The Natural frequency given static deflection (Shaft fixed, uniformly distributed load) formula is defined as set of frequencies at which shaft naturally vibrate is calculated using Frequency = 0.571/(sqrt(Static Deflection)). To calculate Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load), 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 = 3.573*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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