General procedure for finding stiffness in vibration problems

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SUMMARY

The discussion focuses on the general procedure for determining stiffness (k) in single degree of freedom (SDOF) vibration problems. The formula for natural frequency is established as ω=√(k/m). Participants seek a systematic approach to calculate stiffness for various configurations, including a massless bar with springs, an L-shaped bar under gravity, and a water column in a U-shaped test tube. The key takeaway is that stiffness can be defined as the ratio of force to displacement, emphasizing the need for a consistent methodology across different scenarios.

PREREQUISITES
  • Understanding of single degree of freedom (SDOF) systems
  • Familiarity with the concept of natural frequency
  • Knowledge of basic mechanics, including force and displacement
  • Experience with vibration analysis techniques
NEXT STEPS
  • Research methods for calculating stiffness in various mechanical systems
  • Learn about the application of the principle of virtual work in stiffness determination
  • Explore the use of finite element analysis (FEA) for complex structures
  • Study the effects of boundary conditions on natural frequency and stiffness
USEFUL FOR

Mechanical engineers, vibration analysts, and students studying dynamics who are looking to deepen their understanding of stiffness calculations in vibration problems.

bda23
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Hi, I have forgotten quite a bit of my vibration studies, so I have a fairly basic question. Essentially, when you want to find the natural frequency of a single dof system, you use ω=√k/m. However, does anyone know a general procedure (not problem-specific) for finding "k" that is applicable to most SDOF problems. Examples would be something along the lines of a a rigid massless bar, hinged at one end, with a few springs attached and a mass at one end, or a rigid L-shaped bar hinged somewhere and gravity acting, or a water column in a U-shaped test tube (height vibrating with gravity)... I think you get the idea. Basically, I am looking for a series of steps that you would go through in all these situations in order to find the stiffness. Thanks.
 
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Stiffnesss = Force / displacement.

Work out the force on the system when it is moved a small distance from its equilibrium position.
 

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