Procedure for Optimization of Truss Space Structures with Fixed Minimum Vibration Frequency

摘要

This paper deals with the problem of a cantilever truss space structure optimization under a frequency constraint.nThe considered structure, with an attached rigid body at the external free end, is typical of satellite appendages. Thensame value of the lowest vibration frequency of the reference truss structure, with uniform thickness over all thencomponent beams, has been prescribed to prevent possible resonances between satellite and appendages. Anminimum value of the thickness over each component beam of the analyzed truss has been established a priori.nFocusing attention on the dynamic behavior, a numerical procedure (based on the classical Rayleigh–Ritz methodnbut combined with the finite element method) has been used. Polynomial power series expansions have been usednboth for the dynamic variables (displacements and rotations) and for the thickness axial distribution over eachncomponent beam of the truss structure. The classical Euler–Lagrange optimality criterion has been used to find thenrequested solution of each optimization operation, which consists of the search for stationary conditions of thenLagrangian functional. A series of repeated optimization operations have been performed to arrive at the thicknessnoptimized profile within each structural component, with the preestablished minimum value of the beams’ thickness.nIt has also been possible to evaluate the weight reduction.