OPTIMUM DESIGN OF STRUCTURES WITH REGARD TO THEIR VIBRATIONAL CHARACTERISTIC - 4. Type-1-PROBLEMS OF BEAMS SUBJECTED TO AXIAL FORCES.

In the first report, there has been presented a general method of optimum design of structures in which natural frequencies are involved in objective functions and/or conditions of constraints. In the second report, the method are demonstrated in the problems of ″type-1″ (i. e. to find the optimum shapes of structures which gave maximum fundamental natural frequencies under specified total mass). The structural elements having 1- and 2-section-freedoms are taken as concrete objects, and numerical results obtained were discussed in detail from many points of view. In this report, we consider the basic problems of ″type-1″ vibrating beams which are subjected to axial forces as advanced numerical examples of the method presented in the first report. Many numerical results are demonstrated and also discussed in detail. Especially, it is necessary to pay attention to the buckling problems in the case of beams subjected to axial forces and columns with regard to their own weight. The problem of finding the optimum shapes of structures which give maximum fundamental natural frequencies under specified total mass (type-1 problem) is considered for beams subjected to axial forces and for tower-shaped structures (columns) with regard to their weight. Numerical examples are presented and discussed in detail.