Optimization with frequency constraints—limitations

Abstract After outlining an efficient algorithm for designing minimum weight structures for a specified frequency of vibration, the limitations of designing such structures are stressed. It is shown that the amount of material that would be necessary for an optimum bar or a beam of a fixed configuration (length and boundary conditions) to attain an abitrarily prescribed frequency can be disproportionately high, yielding a design that is completely impractical. In some cases there is an upper bound on the maximum frequency that can be attained irrespective of the amount of material used. The effectiveness of configuration changes in conjunction with optimization is emphasized to circumvent this difficulty.