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 beam equations. Using a technique from the mathematics of asymptotic analysis called homogenization, we show how such approximations may be derived in a systematic way which avoids errors made using "direct" averaging methods. We also develop a model for the combined problem of homogenization and control of vibrations in lattice structures and present some preliminary analysis of this problem.