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Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second. Check FAQs
f=3.573⋅E⋅Ishaft⋅gw⋅Lshaft4
f - Frequency?E - Young's Modulus?Ishaft - Moment of inertia of shaft?g - Acceleration due to Gravity?w - Load per unit length?Lshaft - Length of Shaft?

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

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Here is how the Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load equation looks like with Values.

Here is how the Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load equation looks like with Units.

Here is how the Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load equation looks like.

3.0254Edit=3.573⋅15Edit⋅6Edit⋅9.8Edit3Edit⋅4500Edit4
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Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load Solution

Follow our step by step solution on how to calculate Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load?

FIRST Step Consider the formula
f=3.573⋅E⋅Ishaft⋅gw⋅Lshaft4
Next Step Substitute values of Variables
∴ f=3.573⋅15N/m⋅6kg·m²⋅9.8m/s²3⋅4500mm4
Next Step Convert Units
∴ f=3.573⋅15N/m⋅6kg·m²⋅9.8m/s²3⋅4.5m4
Next Step Prepare to Evaluate
∴ f=3.573⋅15⋅6⋅9.83⋅4.54
Next Step Evaluate
∴f=3.0253919978642Hz
LAST Step Rounding Answer
∴f=3.0254Hz

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

Variables
Functions
Frequency
Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second.
Symbol: f
Measurement: FrequencyUnit: Hz
Note: Value can be positive or negative.
Formulas to find FrequencyOpen Variable
Young's Modulus
Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Symbol: E
Measurement: Stiffness ConstantUnit: N/m
Note: Value should be greater than 0.
Formulas to find Young's ModulusOpen Variable
Moment of inertia of shaft
Moment of inertia of shaft can be calculated by taking the distance of each particle from the axis of rotation.
Symbol: Ishaft
Measurement: Moment of InertiaUnit: kg·m²
Note: Value should be greater than 0.
Formulas to find Moment of inertia of shaftOpen Variable
Acceleration due to Gravity
Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Symbol: g
Measurement: AccelerationUnit: m/s²
Note: Value should be greater than 0.
Formulas to find Acceleration due to GravityOpen Variable
Load per unit length
Load per unit length is the distributed load which is spread over a surface or line.
Symbol: w
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Formulas to find Load per unit lengthOpen Variable
Length of Shaft
Length of shaft is the distance between two ends of shaft.
Symbol: Lshaft
Measurement: LengthUnit: mm
Note: Value should be greater than 0.
Formulas to find Length of ShaftOpen Variable
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.
Syntax: sqrt(Number)

Other Formulas to find Frequency

​Go Natural Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)
f=0.571δ

Other formulas in Shaft Fixed at Both Ends Carrying a Uniformly Distributed Load category

​Go Circular Frequency given Static Deflection (Shaft Fixed, Uniformly Distributed Load)
ωn=2⋅π⋅0.571δ
​Go Static Deflection given Natural Frequency (Shaft Fixed, Uniformly Distributed Load)
δ=(0.571f)2
​Go M.I of Shaft given Static Deflection for Fixed Shaft and Uniformly Distributed Load
Ishaft=w⋅Lshaft4384⋅E⋅δ
​Go Length of Shaft in given Static Deflection (Shaft Fixed, Uniformly Distributed Load)
Lshaft=(δ⋅384⋅E⋅Ishaftw)14

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

Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load evaluator uses Frequency = 3.573*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)) to evaluate the Frequency, Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load formula is defined as the frequency at which a shaft fixed at both ends and carrying a uniformly distributed load vibrates freely in a transverse direction, providing a measure of the shaft's natural frequency in free transverse vibrations. Frequency is denoted by f symbol.

How to evaluate Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load using this online evaluator? To use this online evaluator for Natural Frequency of Shaft Fixed at Both Ends and Carrying 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.

FAQs on Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load

What is the formula to find Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load?
The formula of Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load is expressed as Frequency = 3.573*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)). Here is an example- 3.025392 = 3.573*sqrt((15*6*9.8)/(3*4.5^4)).
How to calculate Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load?
With Young's Modulus (E), Moment of inertia of shaft (Ishaft), Acceleration due to Gravity (g), Load per unit length (w) & Length of Shaft (Lshaft) we can find Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load using the formula - Frequency = 3.573*sqrt((Young's Modulus*Moment of inertia of shaft*Acceleration due to Gravity)/(Load per unit length*Length of Shaft^4)). This formula also uses Square Root Function function(s).
What are the other ways to Calculate Frequency?
Here are the different ways to Calculate Frequency-
  • Frequency=0.571/(sqrt(Static Deflection))OpenImg
Can the Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load be negative?
Yes, the Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load, measured in Frequency can be negative.
Which unit is used to measure Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load?
Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load is usually measured using the Hertz[Hz] for Frequency. Petahertz[Hz], Terahertz[Hz], Gigahertz[Hz] are the few other units in which Natural Frequency of Shaft Fixed at Both Ends and Carrying Uniformly Distributed Load can be measured.
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