Equivalent spring constant of rigid bodies

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SUMMARY

The discussion focuses on calculating the equivalent spring constant (ke) for a standing cylinder, which is essential for determining its natural frequency. The formula for ke is given as ke = (EY * s) / (h), where EY represents Young's elastic modulus, s is the cross-sectional area, and h is the height of the cylinder. The user inquires about the derivation of this formula and its applicability to other rigid bodies, such as rectangular prisms. The consensus is that the same principles can be applied to various shapes, provided the correct parameters are used.

PREREQUISITES
  • Understanding of Young's elastic modulus (EY)
  • Knowledge of cross-sectional area calculations
  • Familiarity with natural frequency concepts
  • Basic principles of rigid body mechanics
NEXT STEPS
  • Research the derivation of the equivalent spring constant for different geometries
  • Explore the calculation of natural frequency for various rigid bodies
  • Learn about the application of Young's modulus in structural analysis
  • Investigate the effects of material properties on the dynamic behavior of structures
USEFUL FOR

Mechanical engineers, structural analysts, and students studying dynamics and material properties will benefit from this discussion, particularly those focused on the vibrational analysis of rigid bodies.

mahavidyas
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Hello everyone.

I have a problem...I'm calculating natural frequency of a standing cylinder.
In order to do that, I need the ke - equivalent spring constant of that cylinder.

ke = (EY * s) / (h)

EY is Young's elastic modulus for material cylinder's made of
s is the cross section of cylinder
h is the height of cylinder

The cylinder is not considered "very long".
When I find ke, I don't have any troubles finding the natural frequency.

I just want to know how is this equivalent spring constant derived?
And, is it possible to apply the same approach for other rigid bodies...ie rectangular prism.
 
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