Optimum Building Design for Forced‐Mode Compliance

Abstract

A new dynamic system response quantity, referred to as forced‐mode compliance, is introduced for the forced steady‐state vibration of a shear building model subjected to a harmonic ground motion. An optimum design problem subject to the constraints on forced‐mode compliance, on fundamental natural frequency and on minimum stiffnesses is formulated and the necessary and sufficient conditions for global optimality are derived. It is shown theoretically and through numerical examples that the closed form optimal solution is useful not only for straightforward optimum design but also for controlling other significant dynamical characteristics.