Homogenization and Control of Lattice Structures
Abstract
Under certain natural conditions the dynamics of large, low-mass lattice structures with a regular infrastructure are well approximated by the dynamics of continua (e.g., trusses may be modeled by beam equations). Using a technique from the mathematics of asymptotic analysis called "homogenization," the author shows how such approximations may be derived in a systematic way that avoids errors made using "direct" averaging methods. He also develops a model for the combined problem of homogenization and control of vibrations in lattice structures, and presents some preliminary analyses of this problem. In section 2 he gives an example derived from Bensoussan, Lions, and Papanicolaou (1978) illustrating some of the subtleties of homogenization, particularly in the context of control problems. In section 3 he derives a homogenized representation for the dynamics of a lattice structure undergoing transverse deflections. He shows that the behavior of the lattice is well approximated by the Timenshenko beam equation, and that this equation arises naturally as the limit of the lattice dynamics when the density of the lattice structure goes to infinity in a well-defined way. The problem of vibration control of a lattice is posed and discussed in section 4. In section 5, he derives a diffusion approximation for the thermal conductivity of a one-dimensional lattice structure. This property is useful in analyzing new materials for large space structures. An operational calculus for homogenization is sketched in the Appendix.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 24, 1985
- Accession Number
- ADA451619
Entities
People
- G. L. Blankenship
Organizations
- University of Maryland