  We present a procedure for the systematic estimation of the dispersion
properties of linear discrete systems with periodic time-varying coefficients.
The approach relies on the analysis of a single unit cell, making use of Bloch
theorem along with the application of a harmonic balance methodology over an
imposed solution ansatz. The solution of the resulting eigenvalue problem is
followed by a procedure that selects the eigen-solutions corresponding to the
ansatz, which is a plane wave defined by a frequency-wavenumber pair. Examples
on spring-mass superlattices demonstrate the effectiveness of the method at
predicting the dispersion behavior of linear elastic media. The matrix
formulation of the problem suggests the broad applicability of the proposed
technique. Furthermore, it is shown how dispersion can inform about the dynamic
behavior of time-modulated finite lattices. The technique can be extended to
multiple areas of physics, such as acoustic, elastic and electromagnetic
systems, where periodic time-varying material properties may be used to obtain
non-reciprocal wave propagation.
