On the optimal design of structures subjected to periodic base excitations

This paper considers the optimal apportionment of the stiffness of a building structure modelled as an undamped shear beam when subjected to a periodic base excitation of frequency, ??. A suitable "cost" associated with this stiffness distribution is minimized subject to constraints on the lowest natural frequency of vibration of the system, the base shear generated by the periodic excitations, and the given lower bound stiffness distribution. Closed form solutions for such constrained optimization problems are generally very difficult to obtain; numerical techniques suffer from a host of problems. The paper uses Farkas\´s Theorem to investigate the underlying structure of the optimization problem and obtains closed form solutions in several cases of engineering importance.