Problem Formulation

The formulation of the optimization problem is comprised of the total added damping as an objective function, and an inequality constraint on the upper bound of each of the local performance indices which are computed based on the behavior of the structure, i. e., satisfying the equations of motion of the damped structure. These constraints are repeated for each ground motion record. The damping coefficients which are the design variables are required to be nonnegative and are assigned an upper bound.