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We consider the weighted isotropic relaxed micromorphic model and provide anin depth investigation of the characteristic dispersion curves when theconstitutive parameters of the model are varied. The weighted relaxedmicromorphic model generalizes the classical relaxed micromorphic modelpreviously introduced by the authors, since it features the Cartan-Liedecomposition of the tensors $P_{,t}$ and Curl $P$ in their dev, dev sym, skewand spheric part. It is shown that the split of the tensor $P_{,t}$ in themicro-inertia provide an independent control of the cut-offs of the opticbenches. This is crucial for the future calibration of the relaxed micromorphicmodel on real band-gap metamaterials.  Even if the physical interest of the introduction of the split of the tensorCurl $P$ is less evident than in the previous case, we discuss in detail whichis its effect on the dispersion curves. Finally, we also provide a completeparametric study involving all the constitutive parameters of the introducedmodel, so giving rise to an exhaustive panorama of dispersion curves for therelaxed micromorphic model.

A panorama of dispersion curves for the weighted isotropic relaxed micromorphic model