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Control of a clamped-free beam by a piezoelectric actuator. (English) Zbl 1106.93008
Summary: We consider a controllability problem for a beam, clamped at one boundary and free at the other boundary, with an attached piezoelectric actuator. By Hilbert Uniqueness Method (HUM) and new results on diophantine approximations, we prove that the space of exactly initial controllable data depends on the location of the actuator. We also illustrate these results with numerical simulations.

MSC:
93B05 Controllability
35Q72 Other PDE from mechanics (MSC2000)
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74M05 Control, switches and devices (“smart materials”) in solid mechanics
93C20 Control/observation systems governed by partial differential equations
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