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Boundary stabilization of a microbeam model
Author(s) -
Guzmán Patricio
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6340
Subject(s) - microbeam , deflection (physics) , mathematics , exponential growth , mathematical analysis , boundary value problem , boundary (topology) , classical mechanics , physics , optics
In this paper, we study the boundary stabilization of the deflection of a clamped‐free microbeam, which is modeled by a sixth‐order hyperbolic equation. We design a boundary feedback control, simpler than the one designed in Vatankhah et al, 2 that forces the energy associated to the deflection to decay exponentially to zero as the time goes to infinity. The rate in which the energy exponentially decays is explicitly given.