Uniformly Distributed Load Unit Length given Natural Frequency Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
w = (pi^2)/(4*f^2)*(E*Ishaft*g)/(Lshaft^4)
This formula uses 1 Constants, 6 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Load per unit length - Load per unit length is the distributed load which is spread over a surface or line.
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.
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
Frequency: 90 Hertz --> 90 Hertz No Conversion Required
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
Length of Shaft: 4500 Millimeter --> 4.5 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
w = (pi^2)/(4*f^2)*(E*Ishaft*g)/(Lshaft^4) --> (pi^2)/(4*90^2)*(15*6*9.8)/(4.5^4)
Evaluating ... ...
w = 0.00065519905929432
STEP 3: Convert Result to Output's Unit
0.00065519905929432 --> No Conversion Required
FINAL ANSWER
0.00065519905929432 0.000655 <-- Load per unit length
(Calculation completed in 00.004 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

Uniformly Distributed Load Unit Length given Natural Frequency Formula

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)
w = (pi^2)/(4*f^2)*(E*Ishaft*g)/(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 Uniformly Distributed Load Unit Length given Natural Frequency?

Uniformly Distributed Load Unit Length given Natural Frequency calculator uses 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) to calculate the Load per unit length, The Uniformly Distributed Load Unit Length given Natural Frequency formula is defined as mass per unit length known as linear density. Load per unit length is denoted by w symbol.

How to calculate Uniformly Distributed Load Unit Length given Natural Frequency using this online calculator? To use this online calculator for Uniformly Distributed Load Unit Length given Natural Frequency, enter Frequency (f), Young's Modulus (E), Moment of inertia of shaft (Ishaft), Acceleration due to Gravity (g) & Length of Shaft (Lshaft) and hit the calculate button. Here is how the Uniformly Distributed Load Unit Length given Natural Frequency calculation can be explained with given input values -> 0.000655 = (pi^2)/(4*90^2)*(15*6*9.8)/(4.5^4).

FAQ

What is Uniformly Distributed Load Unit Length given Natural Frequency?
The Uniformly Distributed Load Unit Length given Natural Frequency formula is defined as mass per unit length known as linear density and is represented as w = (pi^2)/(4*f^2)*(E*Ishaft*g)/(Lshaft^4) or 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). Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second, 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 & Length of shaft is the distance between two ends of shaft.
How to calculate Uniformly Distributed Load Unit Length given Natural Frequency?
The Uniformly Distributed Load Unit Length given Natural Frequency formula is defined as mass per unit length known as linear density is calculated using 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). To calculate Uniformly Distributed Load Unit Length given Natural Frequency, you need Frequency (f), Young's Modulus (E), Moment of inertia of shaft (Ishaft), Acceleration due to Gravity (g) & Length of Shaft (Lshaft). With our tool, you need to enter the respective value for Frequency, Young's Modulus, Moment of inertia of shaft, Acceleration due to Gravity & 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 Load per unit length?
In this formula, Load per unit length uses Frequency, Young's Modulus, Moment of inertia of shaft, Acceleration due to Gravity & Length of Shaft. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Load per unit length = (Static Deflection*384*Young's Modulus*Moment of inertia of shaft)/(5*Length of Shaft^4)
  • 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)
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