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Circular Frequency due to Uniformly Distributed Load Calculator

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

✖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.ⓘ Circular Frequency due to Uniformly Distributed Load [ω_n]

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Circular Frequency due to Uniformly Distributed Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
ω_n = pi^2*sqrt((E*I_shaft*g)/(w*L_shaft^4))
This formula uses 1 Constants, 1 Functions, 6 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 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 = pi^2*sqrt((E*I_shaft*g)/(w*L_shaft^4)) --> pi^2*sqrt((15*1.085522*9.8)/(3*3.5^4))

Evaluating ... ...

ω_n = 5.8759895060384

STEP 3: Convert Result to Output's Unit

5.8759895060384 Radian per Second --> No Conversion Required

FINAL ANSWER

5.8759895060384 ≈ 5.87599 Radian per Second <-- Natural Circular Frequency

(Calculation completed in 00.004 seconds)

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Home » Physics » Theory of Machine » Vibrations » Longitudinal and Transverse Vibrations » Natural Frequency of Free Transverse Vibrations » Mechanical » Uniformly Distributed Load Acting Over a Simply Supported Shaft » Circular Frequency due to 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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< Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Length of Shaft given Static Deflection

LaTeX Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)

Uniformly Distributed Load Unit Length given Static Deflection

LaTeX 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

LaTeX Go Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))

Natural Frequency given Static Deflection

LaTeX Go Frequency = 0.5615/(sqrt(Static Deflection))

Circular Frequency due to Uniformly Distributed Load Formula

LaTeX 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))
ω_n = pi^2*sqrt((E*I_shaft*g)/(w*L_shaft^4))

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 Circular Frequency due to Uniformly Distributed Load?

Circular Frequency due to Uniformly Distributed Load calculator uses 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)) to calculate the Natural Circular Frequency, Circular Frequency due to Uniformly Distributed Load formula is defined as the natural frequency of free transverse vibrations of a shaft under uniformly distributed load, which is a critical parameter in mechanical engineering to determine the shaft's vibrational behavior and stability. Natural Circular Frequency is denoted by ω_n symbol.

How to calculate Circular Frequency due to Uniformly Distributed Load using this online calculator? To use this online calculator for Circular Frequency due to 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 Circular Frequency due to Uniformly Distributed Load calculation can be explained with given input values -> 5.87599 = pi^2*sqrt((15*1.085522*9.8)/(3*3.5^4)).

FAQ

What is Circular Frequency due to Uniformly Distributed Load?

Circular Frequency due to Uniformly Distributed Load formula is defined as the natural frequency of free transverse vibrations of a shaft under uniformly distributed load, which is a critical parameter in mechanical engineering to determine the shaft's vibrational behavior and stability and is represented as ω_n = pi^2*sqrt((E*I_shaft*g)/(w*L_shaft^4)) or 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)). 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 Circular Frequency due to Uniformly Distributed Load?

Circular Frequency due to Uniformly Distributed Load formula is defined as the natural frequency of free transverse vibrations of a shaft under uniformly distributed load, which is a critical parameter in mechanical engineering to determine the shaft's vibrational behavior and stability is calculated using 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)). To calculate Circular Frequency due to 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*0.5615/(sqrt(Static Deflection))

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