An Optimal Control Problem for A Viscoelastic Plate in a Dynamic Contact with an Obstacle

Abstract

We deal with an optimal control problem governed by a nonlinear hyperbolic initial-boundary value problem describing the perpendicular vibrations of a simply supported anisotropic viscoelastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. We verify the existence of an optimal thickness function.

An optimal design of an elastic plate in a dynamic contact with a rigid obstacle

“…We have E ad := e ∈ H 2 (Ω) : 0 < e min ≤ e(x) ≤ e max ∀ x ∈Ω, e H 2 (Ω) ≤ê the convex set of admissible thicknesses. We have considered a similar problem for a viscoelastic plate in [1]. In contrast to it the acceleration of the middle surface appears here in a variational formulation of the state problem but only in a form of a measure in the same way as in [2].…”

“…We have considered a similar problem for a viscoelastic plate in [1]. We have considered a similar problem for a viscoelastic plate in [1].…”

An optimal design problem for an anisotropic elastic plate in a dynamic contact with an obstacle

“…The dynamic contact for an isotropic elastic von Kármán plate has been solved in Bock and Jarušek [1] and for a thermoelastic plate in Bock et al [2]. We have considered the problem of the optimal design problem of an anisotropic viscoelastic plate in Bock and Kečkemétyová [3]. In the elastic case, there is a comparision with a viscoelastic plate with less regularity of a solution of a state variational inequality.…”

“…[2]. We have considered the problem of the optimal design problem of an anisotropic viscoelastic plate in Bock and Kečkemétyová [3]. In the elastic case, there is a comparision with a viscoelastic plate with less regularity of a solution of a state variational inequality.…”