Lie-Theory for a One-Dimensional Laminated Composite and the Problem of Homogenization.

摘要

The paper deals with the development of a continuum theory for time-harmonic longitudinal waves propagating in a one-dimensional laminated composite with periodic structure. The development is based on the method of Lie-series and a hierarchy of improved approximate theories are obtained for wavelengths longer than the typical dimensions of the composite microstructure. Effective material properties are also defined and the dispersion spectrum compared with the exact theory, over one Brillouin zone. It is also shown how the effective properties of the laminated, periodic composite can also be obtained by homogenization via a multiple scale expansion. (Author)