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

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Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load General Shaft Shaft Subjected to a Number of Point Loads Uniformly Distributed Load Acting Over a Simply Supported Shaft

✖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.ⓘ Young's Modulus [E]			+10% -10%
✖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.ⓘ Moment of inertia of shaft [I_shaft]			+10% -10%
✖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.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.ⓘ Load per unit length [w]			+10% -10%
✖Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force.ⓘ Natural Circular Frequency [ω_n]			+10% -10%

✖Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.ⓘ Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) [L_shaft]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
L_shaft = ((504*E*I_shaft*g)/(w*ω_n^2))^(1/4)
This formula uses 6 Variables

Variables Used

Length of Shaft - (Measured in Meter) - Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.
Young's Modulus - (Measured in Newton per Meter) - 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.
Moment of inertia of shaft - (Measured in Kilogram Square Meter) - 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.
Acceleration due to Gravity - (Measured in Meter per Square Second) - 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.
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.
Natural Circular Frequency - (Measured in Radian per Second) - Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force.

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: 1.085522 Kilogram Square Meter --> 1.085522 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
Natural Circular Frequency: 13.1 Radian per Second --> 13.1 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_shaft = ((504*E*I_shaft*g)/(w*ω_n^2))^(1/4) --> ((504*15*1.085522*9.8)/(3*13.1^2))^(1/4)

Evaluating ... ...

L_shaft = 3.5353357398968

STEP 3: Convert Result to Output's Unit

3.5353357398968 Meter --> No Conversion Required

FINAL ANSWER

3.5353357398968 ≈ 3.535336 Meter <-- Length of Shaft

(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 » Mechanical » Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load » Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load Calculators

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

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

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

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

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

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

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

LaTeX Go Static Deflection = (0.571/Frequency)^2

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

LaTeX Go

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

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) calculator uses 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) to calculate the Length of Shaft, Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) formula is defined as the distance from one end of a shaft to the other, which is a critical parameter in determining the natural frequency of free transverse vibrations of a shaft under uniformly distributed load when fixed at both ends. Length of Shaft is denoted by L_shaft symbol.

How to calculate Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) using this online calculator? To use this online calculator for Length of Shaft given Natural Circular Frequency (Shaft Fixed, 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) & Natural Circular Frequency (ω_n) and hit the calculate button. Here is how the Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) calculation can be explained with given input values -> 3.535336 = ((504*15*1.085522*9.8)/(3*13.1^2))^(1/4).

FAQ

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

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) formula is defined as the distance from one end of a shaft to the other, which is a critical parameter in determining the natural frequency of free transverse vibrations of a shaft under uniformly distributed load when fixed at both ends and is represented as L_shaft = ((504*E*I_shaft*g)/(w*ω_n^2))^(1/4) or 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). 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, 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, 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, Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations & Natural Circular Frequency is the number of oscillations per unit time of a system vibrating freely in transverse mode without any external force.

How to calculate Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load)?

Length of Shaft given Natural Circular Frequency (Shaft Fixed, Uniformly Distributed Load) formula is defined as the distance from one end of a shaft to the other, which is a critical parameter in determining the natural frequency of free transverse vibrations of a shaft under uniformly distributed load when fixed at both ends is calculated using 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). To calculate Length of Shaft given Natural Circular Frequency (Shaft Fixed, 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) & Natural Circular Frequency (ω_n). 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 & Natural Circular Frequency 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 Length of Shaft?

In this formula, Length of Shaft uses Young's Modulus, Moment of inertia of shaft, Acceleration due to Gravity, Load per unit length & Natural Circular Frequency. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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