Natural Frequency due to Uniformly Distributed Load Solution

STEP 0: Pre-Calculation Summary
Formula Used
Frequency = pi/2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
f = pi/2*sqrt((E*Ishaft*g)/(w*Lshaft^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
Frequency - (Measured in Hertz) - Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Moment of inertia of shaft - (Measured in Kilogram Square Meter) - Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.
Acceleration due to Gravity - (Measured in Meter per Square Second) - Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Load per unit length - Load per unit length is the distributed load which is spread over a surface or line.
Length of Shaft - (Measured in Meter) - Length of shaft is the distance between two ends of 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: 6 Kilogram Square Meter --> 6 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: 4500 Millimeter --> 4.5 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
f = pi/2*sqrt((E*Ishaft*g)/(w*Lshaft^4)) --> pi/2*sqrt((15*6*9.8)/(3*4.5^4))
Evaluating ... ...
f = 1.33005167572341
STEP 3: Convert Result to Output's Unit
1.33005167572341 Hertz --> No Conversion Required
FINAL ANSWER
1.33005167572341 1.330052 Hertz <-- 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 Due to Uniformly Distributed Load Acting Over a Simply Supported Shaft Calculators

Static Deflection at Distance x from End A
Go Static deflection at distance x from end A = (Load per unit length*(Distance of small section of shaft from end A^4-2*Length of Shaft*Distance of small section of shaft from end A+Length of Shaft^3*Distance of small section of shaft from end A))/(24*Young's Modulus*Moment of inertia of shaft)
Natural Frequency due to Uniformly Distributed Load
Go Frequency = pi/2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
Circular Frequency due to Uniformly Distributed Load
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))
Maximum Bending Moment at Distance x from End A
Go Bending Moment = (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
Length of Shaft given Circular Frequency
Go Length of Shaft = ((pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)
Uniformly Distributed Load Unit Length given Circular Frequency
Go Load per unit length = (pi^4)/(Natural Circular Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)
Moment of Inertia of Shaft given Circular Frequency
Go Moment of inertia of shaft = (Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity)
Length of Shaft given Natural Frequency
Go Length of Shaft = ((pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length))^(1/4)
Uniformly Distributed Load Unit Length given Natural Frequency
Go Load per unit length = (pi^2)/(4*Frequency^2)*(Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Length of Shaft^4)
Moment of Inertia of Shaft given Natural Frequency
Go Moment of inertia of shaft = (4*Frequency^2*Load per unit length*Length of Shaft^4)/(pi^2*Young's Modulus*Acceleration due to Gravity)
Length of Shaft given Static Deflection
Go Length of Shaft = ((Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Load per unit length))^(1/4)
Moment of Inertia of Shaft given Static Deflection given Load per Unit Length
Go Moment of inertia of shaft = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)
Static Deflection of Simply Supported Shaft due to Uniformly Distributed Load
Go Static Deflection = (5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Moment of inertia of shaft)
Uniformly Distributed Load Unit Length given Static Deflection
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
Go Natural Circular Frequency = 2*pi*0.5615/(sqrt(Static Deflection))
Natural Frequency given Static Deflection
Go Frequency = 0.5615/(sqrt(Static Deflection))
Static Deflection using Natural Frequency
Go Static Deflection = (0.5615/Frequency)^2

Natural Frequency due to Uniformly Distributed Load Formula

Frequency = pi/2*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4))
f = pi/2*sqrt((E*Ishaft*g)/(w*Lshaft^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 Natural Frequency due to Uniformly Distributed Load?

Natural Frequency due to Uniformly Distributed Load calculator uses 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 Frequency, The Natural frequency due to uniformly distributed load formula is defined as set of frequencies at which they naturally vibrate. Frequency is denoted by f symbol.

How to calculate Natural Frequency due to Uniformly Distributed Load using this online calculator? To use this online calculator for Natural Frequency due to Uniformly Distributed Load, enter Young's Modulus (E), Moment of inertia of shaft (Ishaft), Acceleration due to Gravity (g), Load per unit length (w) & Length of Shaft (Lshaft) and hit the calculate button. Here is how the Natural Frequency due to Uniformly Distributed Load calculation can be explained with given input values -> 1.330052 = pi/2*sqrt((15*6*9.8)/(3*4.5^4)).

FAQ

What is Natural Frequency due to Uniformly Distributed Load?
The Natural frequency due to uniformly distributed load formula is defined as set of frequencies at which they naturally vibrate and is represented as f = pi/2*sqrt((E*Ishaft*g)/(w*Lshaft^4)) or 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 mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation, Acceleration due to Gravity is acceleration gained by an object because of gravitational force, Load per unit length is the distributed load which is spread over a surface or line & Length of shaft is the distance between two ends of shaft.
How to calculate Natural Frequency due to Uniformly Distributed Load?
The Natural frequency due to uniformly distributed load formula is defined as set of frequencies at which they naturally vibrate is calculated using 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 Natural Frequency due to Uniformly Distributed Load, you need Young's Modulus (E), Moment of inertia of shaft (Ishaft), Acceleration due to Gravity (g), Load per unit length (w) & Length of Shaft (Lshaft). 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 Frequency?
In this formula, 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 -
  • Frequency = 0.5615/(sqrt(Static Deflection))
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