Controllability of the Kirchhoff system for beams as a limit of the Mindlin-Timoshenko system. (English) Zbl 1170.74351
Summary: We consider the dynamical one-dimensional Mindlin-Timoshenko system for beams. We analyze how its controllability properties depend on the modulus of elasticity in shear \(k\). In particular we prove that the exact boundary controllability property of the Kirchhoff system may be obtained as a singular limit, as \(k\rightarrow\infty,\) of the partial controllability of projections over a sharp subspace of solutions generated by the eigenfunctions that converge, as \(k\rightarrow\infty\), towards the spectrum of the Kirchhoff system.
MSC:
74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
93B05 | Controllability |
93B07 | Observability |