Optimization of frames and trusses under natural frequency constraints

This paper demonstrates an optimization algorithm of frames and trusses considering natural frequency constraints. The fundamental natural frequency of a structure is required to be greater than or equal to its prescribed value. The optimality criterion method is used to develop a recursive relationship for the weight minimizing problem. This relationship and a single Lagrange multiplier are derived for member groups in the structure. A lumped mass model is adopted in the free vibration analyses and large non-structural masses are imposed on the structures. A number of design examples are presented to demonstrate the application of the algorithm. Optimum designs of the same structures are obtained for various frequency constraints.