Null controllability holds for the beam equation with structural damping ρ for all ρ ≤ 2 and almost all ρ > 2.
Balakrishnan, Damping operators in continuum models of flexible structures: Explicit models for proportional damping in beam bending with end-bodies, Appl
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Boundary null-controllability for the beam equation with classical structural damping
Null controllability holds for the beam equation with structural damping ρ for all ρ ≤ 2 and almost all ρ > 2.