We analyse elastic Bloch-Floquet waves in periodic planar lattices, with micropolar rotations taken into account. This is followed by the study of standing waves corresponding to eigenmodes of certain types and defect modes. Examples include time-harmonic truss and frame structures and systems with rotational springs. The inertial properties of the system are controlled by distributing the mass throughout the junction regions in addition to the elastic links. In the analysis of dispersion properties of Bloch-Floquet waves, we derive analytical asymptotic estimates for the effective group velocities in the acoustic modes to investigate possible morphological corrections. Periodic arrays of defects are introduced by breaking several bonds leading to standing defect modes. Explicit analytical estimates are compared with the results of numerical simulations.