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

STEP 0: Pre-Calculation Summary
Formula Used
Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection))
ωn = (2*pi*0.571)/(sqrt(δ))
This formula uses 1 Constants, 1 Functions, 2 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.
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
ωn = (2*pi*0.571)/(sqrt(δ)) --> (2*pi*0.571)/(sqrt(0.072))
Evaluating ... ...
ωn = 13.3705640380808
STEP 3: Convert Result to Output's Unit
13.3705640380808 Radian per Second --> No Conversion Required
FINAL ANSWER
13.3705640380808 13.37056 Radian per Second <-- Natural Circular Frequency
(Calculation completed in 00.020 seconds)

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National Institute Of Technology (NIT), Hamirpur
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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

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

Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection))
ωn = (2*pi*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 Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?

Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) calculator uses Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection)) to calculate the Natural Circular Frequency, The Circular frequency given static deflection (Shaft fixed, uniformly distributed load) formula is defined as a scalar measure of rotation rate. Natural Circular Frequency is denoted by ωn symbol.

How to calculate Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) using this online calculator? To use this online calculator for Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load), enter Static Deflection (δ) and hit the calculate button. Here is how the Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load) calculation can be explained with given input values -> 13.37056 = (2*pi*0.571)/(sqrt(0.072)).

FAQ

What is Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?
The Circular frequency given static deflection (Shaft fixed, uniformly distributed load) formula is defined as a scalar measure of rotation rate and is represented as ωn = (2*pi*0.571)/(sqrt(δ)) or Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection)). Static deflection is the extension or compression of the constraint.
How to calculate Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)?
The Circular frequency given static deflection (Shaft fixed, uniformly distributed load) formula is defined as a scalar measure of rotation rate is calculated using Natural Circular Frequency = (2*pi*0.571)/(sqrt(Static Deflection)). To calculate Circular 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 Natural Circular Frequency?
In this formula, Natural Circular Frequency uses Static Deflection. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • 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))
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