| Author | Message | ||
     Yury Mukharsky (muh) New member Username: muh Post Number: 1 Registered: 04-2008 |
Is it possible in FlexPDE to model vibrations of a light membrane in non-viscous media with non-negligible density in 3D domain? What would be the approach? One could use internal boundary condition to describe the action of the membrane, but the boundary conditions would be neither natural nor value and I can not think of a way to reduce them to either of the two. | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 1091 Registered: 06-2003 |
We have not specifically done this problem, but I see no reason why it would not succeed. First you need to pose the PDE system mathematically, then write the system in FlexPDE script language. Natural boundary conditions are frequently equivalent to fundamental conservation laws, so it would be surprising if you could not pose the equations in such a way that the "Natural" BC is the natural BC. | ||
| Yury Mukharsky (muh) New member Username: muh Post Number: 2 Registered: 04-2008 |
In the incompressible non-viscous media we have standard div(grad(phi))=0 equation. The membrane (infinitely light, stretched in xy plane) introduces pressure jump across itself, which is proportional to the curvature of the membrane K*(dxx(u)+dyy(u)), where u is the z-displacement of the membrane (moving with the media in z-direction). For oscillatory motion with angular frequency w u=dz(phi)/w. |