There is no slippery condition there, so you can assume it as a fixed position case. it means you should fix all the 6 DoFs there.

Dr. Sadeghnejad,

Thank you for your response. I assume DoF means degrees of freedom. I do not know what a "slippery" condition is. When you say that I should fix all the 6 DoFs at the interface between the two halves of the plate, again, I do not know what you mean.

I am numerically solving  

NL [d4/dx4+2d4/(dx2dy2)+d4/dy4]w + rho*h*d2w/dt2 = 0

in the interior of the left half (0

Dear Prof. Borisyuk.

Thank you for responding.

The plate is an approximation to a piano soundboard that would have a change in board stiffness where the bridges are located.

I am trying to start simply with a rectangular board of length L and height H that is divided at x=L/2 and is glued together. The two halves that are joined at x=L/2 consist of different materials. The edges the board are clamped so that the displacement w(x,y,t) is zero and also dw/dx and dw/dy are zero.

I have numerically solved the problem using finite differences. When I pass into another zone I simply change the parameters occurring in the finite difference approximation of the partial differential equation

NL [d4/dx4+2d4/(dx2dy2)+d4/dy4]w + rho*h*d2w/dt2 = 0.

I am not sure that this is correct and I am wondering if I should apply boundary conditions along x=L/2, 0

By no slippery condition I mean both two different plates can not slide on each other. If you assume 3 DoFs for displacement and 3 DoFs for rotation, you should have a complementary condition in the attached edge.

You are right, you can choose w(L/2-,y)=w(L/2+,y) for 0

Thank you, Dr. Sadeghnejad.

Thank you for your answer!

Prof. Borisyuk,

Thanks for your responses.

I have Morse's books ("Vibration and Sound" and "Theoretical Acoustics"). Regarding details of the plate solution I have Nowicki's "Dynamics of Elastic Systems". I find all of these books to be helpful, especially Nowicki's for this problem. I do not have the Morse and Feshback book although I have other somewhat similar books.

I am trying to numerically simulate the effect of striking a piano string whose bridge is attached to a plate (the soundboard). I am using Giordano's model (from "Computational Physics") for the hammer/string. The plate is simulated by the plate equation (from Nowicki) with a force term coming from the force of the string on the bridge.The simulation results (so far) show that the plate eigenfunctions  compete with and often dominate the harmonic frequencies of the string. Because this is not observed in real life I have been posting on this forum.

See other results on

https://sites.google.com/site/analysisofsoundsandvibrations/

I appreciate your suggestions. I will try to track down your cited publication "Vibration and Sound Radiation by Elastic Elements Excited by Turbulent Flow".

Regards,

Dave