Distributed control of layered orthotropic plates with damping

Optimal control of a composite rectangular plate on an elastic foundation is studied with the objective of minimizing its dynamic response in a given period of time with the minimum possible expenditure of force. The plate undergoes transient vibrations starting from specified initial displacement and velocity distributions, and the control is exercised by optimally determining the transverse distributed force. The multiple objectives of the problem are taken into account by adopting a vector performance criterion comprising quadratic functional of the deflection, velocity and distributed force. The sufficiency condition of optimality is derived using control theory results which lead to an analytic solution of the problem. Numerical results are given for simply supported plates made of specially orthotropic layers of boron-fibre-reinforced plastic material. It is demonstrated that the effectiveness of the proposed control depends on the lamination order, foundation modulus, viscous damping, aspect ratio and terminal time as well as on the weight factors attached to various cost functionals.