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Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying 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%
✖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 [L_shaft]			+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 of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load [ω_n]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
ω_n = sqrt((504*E*I_shaft*g)/(w*L_shaft^4))
This formula uses 1 Functions, 6 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

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.
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.
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.

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
Length of Shaft: 3.5 Meter --> 3.5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω_n = sqrt((504*E*I_shaft*g)/(w*L_shaft^4)) --> sqrt((504*15*1.085522*9.8)/(3*3.5^4))

Evaluating ... ...

ω_n = 13.3658485060139

STEP 3: Convert Result to Output's Unit

13.3658485060139 Radian per Second --> No Conversion Required

FINAL ANSWER

13.3658485060139 ≈ 13.36585 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 » Mechanical » Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load » Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying 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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< 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

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

LaTeX 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))
ω_n = sqrt((504*E*I_shaft*g)/(w*L_shaft^4))

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

Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load calculator uses 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)) to calculate the Natural Circular Frequency, Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load formula is defined as the rate at which a shaft fixed at both ends and carrying a uniformly distributed load vibrates naturally when it is subjected to free transverse vibrations, providing insight into the shaft's dynamic behavior. Natural Circular Frequency is denoted by ω_n symbol.

How to calculate Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load using this online calculator? To use this online calculator for Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying 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 Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load calculation can be explained with given input values -> 13.36585 = sqrt((504*15*1.085522*9.8)/(3*3.5^4)).

FAQ

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

Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load formula is defined as the rate at which a shaft fixed at both ends and carrying a uniformly distributed load vibrates naturally when it is subjected to free transverse vibrations, providing insight into the shaft's dynamic behavior and is represented as ω_n = sqrt((504*E*I_shaft*g)/(w*L_shaft^4)) or 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)). 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 & Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.

How to calculate Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load?

Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load formula is defined as the rate at which a shaft fixed at both ends and carrying a uniformly distributed load vibrates naturally when it is subjected to free transverse vibrations, providing insight into the shaft's dynamic behavior is calculated using 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)). To calculate Natural Circular Frequency of Shaft Fixed at Both Ends and Carrying 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*0.571)/(sqrt(Static Deflection))

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