Dynamic analysis of a lattice structure by homogenization: Experimental validation

Abstract

A homogenization method is presented for dynamic analysis of truss structures motivated by large satellite applications. The proposed method was previously compared to a full finite element procedure and the experimental verification of the homogenization approach is presented here. Local strains in a planar truss are found in terms of the strain components evaluated at the center of the repeating truss element. Kinetic and strain energy expressions are then derived in terms of the spatial and time derivative of the displacement components at the center of the truss element. Necessary assumptions are made to reduce the order of the strain field of the full model to a geometrically reduced order model. Hamilton's principle is employed to find the governing partial differential equations of motion for the equivalent continuum model. It is shown that the dynamic equations for this structure are similar to those of an anisotropic Timoshenko beam theory. Finally the natural frequencies of the structure are found using the one-dimensional homogenized model. A truss structure was fabricated and tested for the purpose of validation of the developed theory. The results for the frequency response functions and the natural frequencies from the continuum model are shown to be in good agreement with the experiment. As a result, the method shows promise as a tool for use in the analysis and design of lattice structures.