Calculating Normal Forces for a Vibrating Beam with Two Impacting Feet

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SUMMARY

This discussion focuses on calculating normal forces for a vibrating beam with two impacting feet. The researcher is investigating how to distribute the total mass of the beam when both feet impact the ground at different accelerations. The formula for normal force, N=(m_totalbeam)*-(accel_foot), applies to a single foot, but the challenge lies in determining how to allocate the mass and calculate the resulting normal forces for each foot when they experience different accelerations. Key considerations include the beam's flexing behavior and the timing of the impacts.

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  • Understanding of ultrasonic vibrations and their effects on structures
  • Familiarity with dynamics and normal force calculations
  • Knowledge of beam theory, particularly free-free beam dynamics
  • Basic principles of structural mechanics and mass distribution
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  • Research "Free-Free Beam Dynamics" to understand the behavior of beams under vibration
  • Study "Normal Force Distribution in Multi-Point Contacts" for insights on mass allocation
  • Explore "Dynamic Response Analysis of Structures" to analyze flexing behavior
  • Investigate "Ultrasonic Vibration Measurement Techniques" for practical applications
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Researchers in mechanical engineering, structural analysts, and anyone involved in the study of vibrating systems and their dynamic responses.

Brazensage
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This has been a bit of a problem for me for a while. My research is in ultrasonic vibrations and this question I have relates to a vibrating beam I am working with. I have a free-free beam vibrating transversely and I know what the accelerations along the beam are. On the beam are feet at two different locations that impact the ground. If there were only one foot impacting the ground I would say that the resulting normal force would simply be:

N=(m_totalbeam)*-(accel_foot)

But since I have two feet how do you divide up the mass? Essentially, if the bar's feet hit the ground with 2 different accelerations, what would each resulting normal force be? Would each foot be 1/2 the total mass times the acceleration of the foot? Would I have to calculate the mass from the foot to the nearest node?
 
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The beam's vibrating in a vertical plane? Is the whole beam moving as a unit or flexing? If flexing, what's the relationship between the instants at which the feet hit the ground (together?). How are the feet positioned as distances from the ends of the bar?
 

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