Homogenization Techniques and Estimation of Material Parameters in Distributed Structures

Abstract

We report here on a part of our continuing efforts on the development of high fidelity dynamic models for composite material structures. The focus of our investigations has been on models to be used in estimation and control of large flexible structures mainly intended for use in space (e.g., antennas, platforms, solar panels, experimental arRays, etc.). At present there is a reasonably adequate understanding of the dynamics of beams and plates made from known materials such as aLuminum alloys. Our recent efforts (see [3] and the references therein) involved models and methods to determine material parameters in composite material structures with simple geometry (beams with attached solid bodies or solid plates). These result in inverse problems that are computationally tractable as long as the physical geometry is relatively simple. However, substantial difficulties arise in cases involving more complex geometries such as grids (which may be viewed as plates with many holes) and trusses (solid coLumns from which most of the material is removed in some periodic, regular fashion). In these cases the difficulties associated with unknown composite material characteristics such as stiffness and internal damping are combined with severe difficulties related to computational grid selection for a domain that is mostly holes or perforations.