AbstractThe problem of damping out the oscillations of a simply supported beam subject to viscous damping is solved analytically by employing a maximum principle. The basic control problem is to minimize the deflection and the velocity of displacements in a given period of time with the minimum possible expenditure of force. The multiobjective problem is scalarized by using a linear combination of the criteria. This problem is also solved by two heuristic approaches: a direct method and an integral equation approach.