FormulaDen logo
FormulaDen.com
Search
Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health
Fx Copy
LaTeX Copy
Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior. 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

With values
With units
Only example

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.

2.1272Edit=3.573⋅15Edit⋅1.0855Edit⋅9.8Edit3Edit⋅3.5Edit4
Solution
Copy
Reset
Share
You are here -

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⋅1.0855kg·m²⋅9.8m/s²3⋅3.5m4
Next Step Prepare to Evaluate
∴ f=3.573⋅15⋅1.0855⋅9.83⋅3.54
Next Step Evaluate
∴f=2.12722918283917Hz
LAST Step Rounding Answer
∴f=2.1272Hz

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

Variables
Functions
Frequency
Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior.
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 measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.
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 is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.
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 the rate of change of velocity of an object under the influence of gravitational force, affecting natural frequency of free transverse vibrations.
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 force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.
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 from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.
Symbol: Lshaft
Measurement: LengthUnit: m
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- 2.127229 = 3.573*sqrt((15*1.085522*9.8)/(3*3.5^4)).
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 (sqrt) 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.
About | Contact | Disclaimer | Terms | Privacy Policy
© 2024. Developed & Maintained by softUsvista Inc.
Copied!