  We report the finding of the analogous valley Hall effect in phononic systems
arising from mirror symmetry breaking, in addition to spatial inversion
symmetry breaking. We study topological phases of plates and spring-mass models
in Kagome and modified Kagome arrangements. By breaking the inversion symmetry
it is well known that a defined valley Chern number arises. We also show that
effectively, breaking the mirror symmetry leads to the same topological
invariant. Based on the bulk-edge correspondence principle, protected edge
states appear at interfaces between two lattices of different valley Chern
numbers. By means a plane wave expansion method and the multiple scattering
theory for periodic and finite systems respectively, we computed the Berry
curvature, the band inversion, mode shapes and edge modes in plate systems. We
also find that appropriate multi-point excitations in finite system gives rise
to propagating waves along a one-way path only.
