Optimal damper placement for planar building frames using transfer functions

A systematic procedure is proposed for finding the optimal damper positioning to minimize the dynamic compliance of a planar building frame. The dynamic compliance is expressed in terms of the transfer function amplitudes of the interstorey drifts evaluated at the undamped fundamental natural frequency. The dynamic compliance is minimized subject to a constraint on the sum of the damping coefficients of added viscous dampers. Optimality criteria are derived and the optimal damper positioning is determined based on a proposed steepest direction search algorithm. This algorithm allows one to find an optimal damper positioning sequentially for gradually increasing total damper capacity levels. Numerical results including comparison with the corresponding uniform damper placement demonstrate the usefulness and validity of this procedure.