  A spectrally formulated finite element analysis based methodology has been
proposed to calculate phononic band structure of reticulated honeycomb lattices
having translationally invariant repetitive elements called unit cells. Bloch
formulation captures dynamics of infinite structure through that of a unit
cell. While conventional FEM is generally used for analyzing dynamics of such
unit systems, here, constituent structural members are treated as 1D waveguide
and modeled as Timoshenko beam frame element, enabling application of spectral
FEM, suitable for accurately analyzing the dynamics, particularly efficient at
very high frequencies. Using exact solutions as shape functions spares dense
meshing. Resulting eigenvalue problem is solved by Wittrick-Williams method, an
iterative scheme. Subsequently, band structures are obtained for supercells-
units comprising multiple elemental unit cells; compared and reconciled with
those obtained using elemental cell (termed primitive unit cell to distinguish
from supercell). Primitive cell band structures are reconstructed from
Supercell band structures. Supercell band structures show some spurious bands,
which are explained in terms of band folding in the primitive cell band
structure. Supercell allows treatment of defects as a periodic feature with
certain defect density. Of particular observation in such band structures is
the separation of bands, known as degeneracy breaking.
