Abstract
Design problems of a beam with a maximum eigenfrequency of an arbitrary prescribed order are described. Two types of optimization problems are formulated and solved. The first is tansverse shape optimization and the second optimization of the mixture rate distribution. In the second problem, it is assumed that the beam is made from two materials and has a uniform transverse shape. The characteristic equation with respect to the eigenfrequency is derived from the well-known Hamilton's principle and is discretized by the finite element method. For solving the optimization problems, the constructive algorithm proposed by the authors is used. The optimal transverse shape and the optimal mixture rate distribution along the beam axis are given as a piecewise linear function.
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