  We report the emergence of electronic edge states in time-periodically driven
strained armchair terminated graphene nanoribbons. This is done by considering
a short-pulse spatial-periodic strain field. Then, the tight-binding
Hamiltonian of the system is mapped into a one dimensional ladder. The time
periodicity is considered within the Floquet formalism. Thus the quasienergy
spectrum is found numerically by diagonalizing the evolution operator. For some
particular cases, the quasienergy spectrum is found analytically. We find that
the system is able to support gapless and gapped phases. Very different edge
states emerge for both the gapless and the gapful phases. In the case of the
gapped phase, edge states emerge at the gap centered at zero quasienergy,
although the Chern number is zero due to the chiral symmetry of the system. For
the gapless phase, besides edge states at zero quasienergy, cosine like edge
states which merge and coexist with the bulk band are observed. To confirm the
topological nature of these edge states, we analytically obtained the effective
Hamiltonian and its spectrum for a particular case, finding that the edge
states are topologically weak. Finally, we found analytically the evolution of
band edges and its crossings as a function of the driven period. Topological
modes arise at such crossings.
