Band structure of a rotating helical phononic crystal

Carlos I. Mendoza , 1,* J. Adrián Reyes,2 and Gerardo J. Vázquez 2

1Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Mexico City, Mexico 2Departamento de Física Química, Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico

We consider an elastic helical medium whose tensor stiffness twirls uniformly along the helix axis. We are

interested in analyzing the band structure when the whole material is externally forced to rotate around the helix

axis to a fixed constant frequency. Departing from a general dynamic description of the elastic phenomena,

we establish a set of equations for the displacement vector and the stress tensor. These equations allow us to

calculate the band structure parametrized by the externally imposed rotating frequency. We find that the band

structure strongly depends on the rotation frequency, and we show that backward and forward modes propagate

differently, particularly for the longitudinal and right-polarized modes.