On the exponential decay of the Euler–Bernoulli beam with boundary energy dissipation☆

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Abstract

We study the asymptotic behavior of the Euler–Bernoulli beam which is clamped at one end and free at the other end. We apply a boundary control with memory at the free end of the beam and prove that the “exponential decay” of the memory kernel is a necessary and sufficient condition for the exponential decay of the energy.

Keywords

Euler–Bernoulli beam
Boundary control
Boundary conditions of memory type
Exponential stability
Semigroup theory

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Research performed under the auspices of G.N.F.M.-I.N.d.A.M. and partially supported by Italian M.I.U.R.

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