Buckling and vibration of periodic lattice structures
Abstract
Lattice booms and platforms composed of flexible members or large diameter rings which may be stiffened by cables in order to support membranelike antennas or reflector surfaces are the main components of some large space structures. The nature of these structures, repetitive geometry with few different members, makes possible relatively simple solutions for buckling and vibration of a certain class of these structures. Each member is represented by a stiffness matrix derived from the exact solution of the beam column equation. This transcendental matrix gives the current member stiffness at any end load or frequency. Using conventional finite element techniques, equilibrium equations can be written involving displacements and rotations of a typical node and its neighbors. The assumptions of a simple trigonometric mode shape is found to satisfy these equations exactly; thus the entire problem is governed by just one 6 x 6 matrix equation involving the amplitude of the displacement and rotation mode shapes. The boundary conditions implied by this solution are simple supported ends for the column type configurations.
 Publication:

Large Space Systems Technology, 1980
 Pub Date:
 February 1981
 Bibcode:
 1981lsst....2...35A
 Keywords:

 Booms (Equipment);
 Buckling;
 Equilibrium Equations;
 Large Space Structures;
 Lattice Vibrations;
 Periodic Variations;
 Stiffness Matrix;
 Finite Element Method;
 Structural Analysis;
 Transcendental Functions;
 Launch Vehicles and Space Vehicles