I would call this a coffered ceiling. You'll need to think about how you want this detail to correspond to your kitchen cabinets. Will you stop the cabinets shy of the ceiling in order to accommodate the beams? Or will you terminate the beam into the crown moulding of the cabinet. I think with a 9' ceiling, your best bet is to terminate them into the crown moulding in order to not chop up elevation. Hope that helps!

We just completed having this type of ceiling installed in our dining room along with the chair rail and the wall framing. I asked for help this morning on the painting and BR Interior Designs was nice enough to help me out. We upgraded our dining room based on this photo. We have 9 foot ceilings and this treatment worked out fantastic. We have a very traditional home. If you can work this into your kitchen, go for it, I think you will be very happy with the result. Good luck.

Thank you for your response.