OPTIMALITY CRITERION FOR MAXIMUM FUNDAMENTAL-FREQUENCY OF FREE-VIBRATIONS OF FRAMES INCLUDING AXIAL AND BENDING EFFECTS

An optimality criterion for maximum multiple fundamental frequency of free vibrations for structures of prescribed weights is presented. The criterion includes both axial and bending effects and can be used for analysis of truss, beam and frame structures. The error norm based on the criterion is proposed and used to verify trial designs against th e optimum. The accompanying iterative procedure reduces this error nor m to zero and drives a trial design to the optimum. The modality of th e design at the optimum and the corresponding set of Lagrange multipli ers are determined automatically.