Wave attenuation, filtering and guiding is an ongoing topic of scientific research, as there are many opportunities for improvement of existing solutions in modern industry. One of the recent advancements has been made with the use of non-reciprocal metamaterials.Certain properties of metamaterials have made them suitable for use in various engineering fields. In this study, we investigate non-reciprocal wave propagation behavior in coupled thin beams phononics, due to time-modulation of material properties and axial loads. We compare the results for the beams which are interconnected with Winkler's type of elastic layers and elastic or viscoelastic Pasternak layers. An analytic approach is used to discover directional band gaps and investigate wave propagation through these systems of beams, at relevant excitation frequencies. The proposed framework can be exploited in further analysis of phononic systems based on multiple beams coupled through different mediums and structural elements modeled with higher-order beam theories.