Shafts -Natural Frequencies / Whirling speeds

Purpose of Calculation
Simple calculations for obtaining the natural frequency  of traverse vibration of shafts and beams which are equal to the shaft whirling speeds.

Calculation Reference
Roymech.co.uk.https://roymech.co.uk/Useful_Tables/Vibrations /Natural_Vibrations.html

Calculation Validation
Background information on the theory is provided on my website  Roymech.org

Important Note:Please only enter data in the identified coloured cells.

Introduction
The calculations below are simple calculations to establish the natural frequency of traverse vibration of shafts .  It can be easily proved that the naturalfrequency of a shaft is equal to the whirling speed. Whirling is a result of resonance when the shaft rotates at the same speed as one of the shafts natural frequencies of transverse vibration. At this speed the shaft will  whirl at an increasing rate . Increasing or reducing the speed will eliminated the whirling effect.

The calculations are all based on the assumption that the beams are round bars of uniform diameter.
The calculations are only for the lower four modes of vibration.

List Of Calcs

1. Cantilever beam / Cantilever shaft on long bearing.
   
2. Simply supported beam . Shaft supported between bearing providing minimum angular restraint
   
3. Beam with fixed end . Shaft supported between long bearings with angular restraint.
   
4. Beam / Shaft with one end fixed and the other simply supported
   
5. Beam/ shaft with one end fixed and the other end carrying a significant mass
   
6. Beam /Shaft simply supported at both ends with a significant mass in the middle
   
7. Beam /Shaft simply supported at both ends with a significant mass at some point along its length
   8)Beam  /Shaft carrying a number of descrete masses

   Calculation Reference
   Mechanical Engineers Data Handbook Carvill Butterworth
   

Roark's Formulas for Stress and Strain

Vibration Handbook