Optimum frequency of structures

I integrated structural and mechanical systems, the design criteria may be governed by the fundamental frequency of the structure either to provide a certain precision in control or to prevent damage to the system due to resonance between the mechanical and structural systems. Tracking antennas, radio telescopes, and orbiting reflectors are a few examples of the types of structures for which the frequency consideration becomes exceptionally important. . Turner attempted to minimize the mass of a structure with a specific natural frequency. This problem is governed by a system of nonlinear equations and a solution was obtained iteratively by an adaptation of the Newton-Ralphson method. The procedure consists essentially of starting with a given mass distribution, and hence with a given natural frequency, and then obtaining a series of corrections to the mass distribution until minimum mass is achieved. In many physical problems, the original frequency may not be satisfactory and, hence, the problem of maximization of frequency for a given total mass of the structure becomes important/The objective of this paper is to present a method for the maximization of the lowest natural frequency of a structural system of a given weight by varying the stiffness of its component elements. This problem has been investigated by Taylor for the special case of a bar.