Optimum Design of Structures with Regard to Their Vibration Characteristic : 3rd Report, The Type-2-problems of Rods and Cantilevers, and Reciprocal Relation between Two Basic Types of Problems

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In the first report, there has been presented a general method of optimum designs of structures in which natural frequencies are involved in objective functions and/or conditions of constraints. In the second report, the method was demonstrated in the type-1-problems, which is one of basic problems of frequency maximization. Concrete objects were taken from structural elements having 1- and 2-section-freedom^<****> and numerical results obtained there were discussed in detail from many points of view. In this report, another basic type-w-problem (i.e. the problem of finding the optimum shapes of structures which give minimum total mass under specified fundamental frequencies) are treated numerically by our same method, taking example of vibrating rods and cantilevers with a point mass. Moreover, reciprocal relations between type-1-problem and type-2-problem are also clarified analytically in discrete systems and continuous ones, and the relations are verifyed numerically by making use of the results in rods and cantilevers.
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