Intrinsic critical speed of a steel circular shaft

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SUMMARY

The intrinsic first critical speed of a circular steel shaft supported by two bearings can be determined using the Rayleigh Method and Dunkerley's Equation. The modulus of elasticity (E) for steel is 207 GPa, and the density of steel must be referenced to calculate the mass of the shaft. The critical speed calculation requires analyzing the shaft's deflection between the bearings and considering the three distinct regions of the shaft to identify the lowest critical speed.

PREREQUISITES
  • Understanding of Rayleigh Method for critical speed calculation
  • Familiarity with Dunkerley's Equation for shaft analysis
  • Knowledge of material properties, specifically the density of steel
  • Basic concepts of static analysis and deflection in mechanical systems
NEXT STEPS
  • Research the density of steel to calculate the mass for critical speed equations
  • Study the Rayleigh Method in detail for dynamic analysis of shafts
  • Explore Dunkerley's Equation applications in mechanical engineering
  • Learn about static analysis techniques for determining deflection in beams and shafts
USEFUL FOR

Mechanical engineers, students studying dynamics and vibrations, and anyone involved in the design and analysis of rotating machinery will benefit from this discussion.

Mechatroni
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Homework Statement


Determine the intrinsic first critical speed of a circular steel shaft supported by two bearings
E=207GPa

How can i determine it I'm very confused about this question , you can see the question at the attachment. Thanks for the help
 

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Specifically, what are you confused about? Do you understand how to calculate the critical speed of a shaft? Have you been exposed to the Rayleigh Method? Dunkerley's equation?
 
i'm not so good at this lecture. The part I'm confused is there is 3 different regions in the shaft so do i have to calculate for each of them and take the lowest one? i know the Rayleigh Method and the Dunkerley's Equation but i need to use m ( mass ) in those equations , the problem is only E is given to me. Where do i have to start to solve this
 
The OP says it is a steel shaft, so you can look up the density of steel and figure the mass of the shaft.

I think your first order of business is to analyze the shaft statically and determine its deflection between the bearings.
 

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