  We consider the effect of periodic scalar and vector potentials generated by
periodic deformations of the graphene crystal lattice, on the energy spectrum
of electrons. The dependence of electron velocity near the Dirac point on the
periodic perturbations of different types is discussed. We also investigated
the effect of screening of the scalar potential by calculating the dielectric
function as a function of the wave length of the periodic potential. This
calculation shows that the periodic scalar field is strongly suppressed by the
screening. Using the dependence of electron velocity on the periodic field we
also studied the variation of the plasmon spectra in graphene. We found that
the spectrum of plasmon excitations can be effectively controlled by the
periodic strain field.
