# What are the boundary conditions for this plate/ring system?

#### LauraMorrison

1. The problem statement, all variables and given/known data

I have a metal disc adhesively bonded at its edges to a piezoelectric ring. The piezoelectric ring vibrates radially which leads to the plate vibrating transversely. I am looking to work out the resonant frequency of the metal disc which I believe will depend on the material properties and dimensions of the disc as well as the vibration of the ring.

2. Relevant equations

What would be the boundary condition for the disc bonded to the vibrating ring in this way? Would it be either clamped or simply supported or something else altogether?

3. The attempt at a solution

My initial thoughts were that the boundary condition would be a clamped one. Further thinking on this made me confused since the ring is moving in and out radially and therefore the displacement of the disc around its edge is not technically equal to zero. I'm not sure if this makes a difference to the boundary condition definition and would really appreciate any clarification.

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#### Dr.D

Why would radial vibration of the ring lead to transverse motion of the disk? Aren't those two motions perpendicular to each other? Perhaps a figure might help here.

"What are the boundary conditions for this plate/ring system?"

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