Distributed control is an effective method for controlling and suppressing
excessive vibrations of continuous systems. Optimal distributed control for
a plate problem is solved utilizing a maximum principle after the introduc
tion of a quadratic index of performance in terms of displacement, velocity
and a control force as well as an adjoint variable. The problem is reduced
to solving a system of partial differential equations for the state variab
le and the adjoint variable subjected to boundary, initial and terminal con
ditions. A numerical algorithm is presented to solve the optimal distribute
d control problem in the space-time domain which reduces the computational
effort required to solve the initial-terminal-boundary, value problem. Resu
lts obtained for a simply supported rectangular, thin plate are also presen
ted.