Dunkerley's Empirical Formula, for Natural Frequency of Whole System Solution

STEP 0: Pre-Calculation Summary
Formula Used
Frequency = 0.4985/sqrt(Static deflection due to point load+Static deflection due to uniform load/1.27)
f = 0.4985/sqrt(δ1+δs/1.27)
This formula uses 1 Functions, 3 Variables
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.
Static deflection due to point load - (Measured in Meter) - Static deflection due to point load is the degree to which a structural element is displaced under a load (due to its deformation).
Static deflection due to uniform load - (Measured in Meter) - Static deflection due to uniform load is the degree to which a structural element is displaced under uniform load (due to its deformation).
STEP 1: Convert Input(s) to Base Unit
Static deflection due to point load: 0.9 Millimeter --> 0.0009 Meter (Check conversion here)
Static deflection due to uniform load: 0.7 Millimeter --> 0.0007 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
f = 0.4985/sqrt(δ1s/1.27) --> 0.4985/sqrt(0.0009+0.0007/1.27)
Evaluating ... ...
f = 13.0859228498128
STEP 3: Convert Result to Output's Unit
13.0859228498128 Hertz --> No Conversion Required
FINAL ANSWER
13.0859228498128 13.08592 Hertz <-- Frequency
(Calculation completed in 00.004 seconds)

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3 Natural Frequency of Free Transverse Vibrations For a Shaft Subjected to a Number of Point Loads Calculators

Dunkerley's Empirical Formula, for Natural Frequency of Whole System
Go Frequency = 0.4985/sqrt(Static deflection due to point load+Static deflection due to uniform load/1.27)
Natural Frequency of Transverse Vibration due to Uniformly Distributed Load
Go Frequency = 0.5615/(sqrt(Static deflection due to uniform load))
Natural Frequency of Transverse Vibration due to Point Load
Go Frequency = 0.4985/(sqrt(Static deflection due to point load))

Dunkerley's Empirical Formula, for Natural Frequency of Whole System Formula

Frequency = 0.4985/sqrt(Static deflection due to point load+Static deflection due to uniform load/1.27)
f = 0.4985/sqrt(δ1+δs/1.27)

What is natural frequency?

Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving or damping force. The motion pattern of a system oscillating at its natural frequency is called the normal mode (if all parts of the system move sinusoidally with that same frequency).

How to Calculate Dunkerley's Empirical Formula, for Natural Frequency of Whole System?

Dunkerley's Empirical Formula, for Natural Frequency of Whole System calculator uses Frequency = 0.4985/sqrt(Static deflection due to point load+Static deflection due to uniform load/1.27) to calculate the Frequency, Dunkerley's Empirical Formula, for Natural Frequency of Whole System, is approximately equal to the sum of the reciprocals of the natural frequencies squared. Frequency is denoted by f symbol.

How to calculate Dunkerley's Empirical Formula, for Natural Frequency of Whole System using this online calculator? To use this online calculator for Dunkerley's Empirical Formula, for Natural Frequency of Whole System, enter Static deflection due to point load 1) & Static deflection due to uniform load s) and hit the calculate button. Here is how the Dunkerley's Empirical Formula, for Natural Frequency of Whole System calculation can be explained with given input values -> 13.08592 = 0.4985/sqrt(0.0009+0.0007/1.27).

FAQ

What is Dunkerley's Empirical Formula, for Natural Frequency of Whole System?
Dunkerley's Empirical Formula, for Natural Frequency of Whole System, is approximately equal to the sum of the reciprocals of the natural frequencies squared and is represented as f = 0.4985/sqrt(δ1s/1.27) or Frequency = 0.4985/sqrt(Static deflection due to point load+Static deflection due to uniform load/1.27). Static deflection due to point load is the degree to which a structural element is displaced under a load (due to its deformation) & Static deflection due to uniform load is the degree to which a structural element is displaced under uniform load (due to its deformation).
How to calculate Dunkerley's Empirical Formula, for Natural Frequency of Whole System?
Dunkerley's Empirical Formula, for Natural Frequency of Whole System, is approximately equal to the sum of the reciprocals of the natural frequencies squared is calculated using Frequency = 0.4985/sqrt(Static deflection due to point load+Static deflection due to uniform load/1.27). To calculate Dunkerley's Empirical Formula, for Natural Frequency of Whole System, you need Static deflection due to point load 1) & Static deflection due to uniform load s). With our tool, you need to enter the respective value for Static deflection due to point load & Static deflection due to uniform load 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 Static deflection due to point load & Static deflection due to uniform load. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Frequency = 0.5615/(sqrt(Static deflection due to uniform load))
  • Frequency = 0.4985/(sqrt(Static deflection due to point load))
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