Calculating Normal Forces for a Vibrating Beam with Two Impacting Feet

[Brazensage]

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?

 

[haruspex]

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?