Calculating Normal Forces for a Vibrating Beam with Two Impacting Feet

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In summary, the speaker's research is focused on ultrasonic vibrations and they are trying to determine the normal force on a vibrating transverse beam with two feet impacting the ground. They know the accelerations along the beam and are wondering how to divide up the mass between the two feet. They also have questions about the relationship between the instants at which the feet hit the ground and how the feet are positioned along the beam.
  • #1
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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  • #2
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?
 

FAQ: Calculating Normal Forces for a Vibrating Beam with Two Impacting Feet

1. What is meant by "Bar hit with 2 accelerations"?

When we say "bar hit with 2 accelerations", it refers to a scenario where a bar or object experiences two different accelerations in a given time period. This could happen due to various factors such as external forces acting on the object or changes in its own velocity.

2. How does the acceleration of the bar affect its motion?

The acceleration of a bar can greatly impact its motion. If the bar experiences a positive acceleration, it will increase its velocity and move in the direction of the acceleration. On the other hand, a negative acceleration will decrease the velocity and cause the bar to move in the opposite direction of the acceleration.

3. What is the difference between acceleration and velocity?

Acceleration and velocity are both measures of an object's motion, but they are different concepts. Velocity refers to the rate of change of an object's position, while acceleration refers to the rate of change of an object's velocity. In simple terms, velocity tells us how fast an object is moving, while acceleration tells us how much the velocity is changing.

4. Can an object have two different accelerations at the same time?

Yes, it is possible for an object to have two different accelerations at the same time. This can happen when there are multiple forces acting on the object, causing it to experience different accelerations in different directions. For example, a car moving in a circular motion will experience both a centripetal acceleration towards the center and a tangential acceleration along its path.

5. How is acceleration measured?

Acceleration is typically measured in meters per second squared (m/s^2). This unit represents the change in velocity over time. To calculate the acceleration of an object, we divide the change in velocity by the time it takes for that change to occur.

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