We deal with an optimal control problem governed by a nonlinear hyperbolic initial-boundary value problem describing the perpendicular vibrations of a clamped beam against a u elastic foundation. A variable thickness of a beam plays the role of a control variable. The original equation for the deflection is regularized in order to derive necessary optimality conditions

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.

ABSTRACT. We deal with the optimal control problem governed by a hyperbolic variational inequality describing the perpendicular vibrations of a beam clamped on the left end with a rigid obstacle at the right end. A variable thickness of a beam plays the role of a control parameter.

We deal with an optimal design problem governed by an initial-boundary value problem for a hyperbolic variational inequality describing the perpendicular vibrations of a simply supported anisotropic elastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. The set of admissible thicknesses for the design problem consists of solutions of a state problem gained as limits of the sequences of functions solving penalized problems.