  In this paper, we use spectral methods by introducing the Bloch waves to
study the homogenization process in the non-periodic class of generalized
Hashin-Shtrikman micro-structures \cite[page no. 281]{T}, which incorporates
both translation and dilation with a family of scales, including one subclass
of laminates. We establish the classical homogenization result with providing
the spectral representation of the homogenized coefficients. It offers a new
lead towards extending the Bloch spectral analysis in the non-periodic,
non-commutative class of micro-structures.
