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In-plane wave propagation in a periodic rectangular grid beam structure,which includes rotational inertia (so-called 'Rayleigh beams'), is analyzedboth with a Floquet-Bloch exact formulation for free oscillations and with anumerical treatment (developed with PML absorbing boundary conditions) forforced vibrations (including Fourier representation and energy fluxevaluations), induced by a concentrated force or moment. A complex interplay isobserved between axial and flexural vibrations (not found in the commonidealization of out-of-plane motion), giving rise to several forms of vibrationlocalization: 'X-', 'cross-' and 'star-' shaped, and channel propagation. Theselocalizations are triggered by several factors, including rotational inertiaand slenderness of the beams and the type of forcing source (concentrated forceor moment). Although the considered grid of beams introduces an orthotropy inthe mechanical response, a surprising 'isotropization' of the vibration isobserved at special frequencies. Moreover, rotational inertia is shown to'sharpen' degeneracies related to Dirac cones (which become more pronouncedwhen the aspect ratio of the grid is increased), while the slenderness can betuned to achieve a perfectly flat band in the dispersion diagram. The obtainedresults can be exploited in the realization of metamaterials designed tocontrol wave propagation.

Free and forced wave propagation in a Rayleigh-beam grid: flat bands, Dirac cones, and vibration localization vs isotropization