Design of minimum mass structures with specified natural frequencies.

A numerical procedure is developed for proportioning the members of an elastic structure so that one or more of its natural frequencies assume given values and the total structural mass is a minimum. It is assumed that the structure is required to support nonstructural masses and that the vibratory inertia loads due to structural masses must be of appreciable magnitude relative to those generated by nonstructural masses. The principal development is based on a finite element idealization and matrix formulation in which the inertia and stiffness matrices of each structural element are proportional to the mass of the element. Lagrange multipliers are employed to introduce the free vibration equations as constraint conditions.