  This paper presents phononic band-structure calculation results obtained
using a mixed variational formulation for 1-, and 2-dimensional unit cells. The
formulation itself is presented in a form which is equally applicable to
3-dimensiomal cases. It has been established that the mixed-variational
formulation presented in this paper shows faster convergence with considerably
greater accuracy than variational principles based purely on the displacement
field, especially for problems involving unit cells with discontinuous
constituent properties. However, the application of this formulation has been
limited to fairly simple unit cells. In this paper we have extended the scope
of the formulation by employing numerical integration techniques making it
applicable for the evaluation of the phononic band-structure of unit cells
displaying arbitrary complexity in their Bravais structure and in the shape,
size, number, and anisotropicity of their micro-constituents. The approach is
demonstrated through specific examples
