On the exact and partial controllability of a membranal cylindrical arch
Event details
| Date | 10.12.2008 |
| Hour | 14:15 |
| Speaker | Prof. Arnaud MÜNCH |
| Location |
MAA110
|
| Category | Conferences - Seminars |
We consider the dynamical system y00 + AMy = 0 - where AM is a mixed order operator with essential spectrum - Modeling the linear membranal vibration of a cylindrical elastic arch with radius of curvature r. y = (y1; y3) denotes the tangential and normal displacement. We examine in this work the null controllability by acting only on the tangential component y1 on the boundary. Using a spectral analysis and Ingham type theorem, we show that the arch is controllable if and only if the initial condition (y0; y1) belongs to the orthogonal of KerAM. Then, we show that the partial controllability problem, which consists to drive only the first component y1 - holds uniformly with respect to the initial data. We also discussed the behavior of the control with respect to the curvature of the arch as well as the Neumann case. Numerical simulations, in full agreement with the theoretical part, complete the study.
Practical information
- General public
- Free