simplified modeling and more effective conception of engineering devices allowing to stop wave propagation in suitable frequency bands. Continuum models are, in fact, suitable to be used as input in finite element calculations, which are for sure one of the main basis of engineering design.

In this paper, we propose to use the relaxed micromorphic continuum model presented in [@NeffRelaxed] to study wave propagation in microstructured materials exhibiting exotic properties with respect to wave propagation. The used kinematics is enhanced with respect to the one used for classical Cauchy continua by means of supplementary kinematical fields with respect to the macroscopic displacement. The introduced supplementary kinematical fields allow to account for the presence of microstructure on the overall mechanical behavior of considered continua. The considered extended kinematics has a similar form as the one used to describe phenomena of energy trapping in internal degrees of freedom (see e.g. [@Carcaterra] and references there cited). However, the aforementioned papers deal with damped systems differently from what done in the present paper where only conservative systems are considered.

It is well known that the mechanical behavior of isotropic Mindlin-Eringen media is, in general, described by means of 18 elastic constants (see [@Mindlin; @EringenBook; 