  The combined effect due to mechanical strain, coupling to the plasmons in a
doped conducting substrate, the plasmon-phonon scattering in conjunction with
the role played by encapsulation of a secondary two-dimensional (2D) layer is
investigated both theoretically and numerically. The calculations are based on
the random-phase approximation (RPA) for the surface response function which
yields the plasmon dispersion equation that is applicable in the presence or
absence of an applied uniaxial strain. We present results showing the
dependence of the frequency of the charge density oscillations on the strain
modulus and direction of the wave vector in the Brillouin zone. The shielding
of a dilute distribution of charges as well as the rate of loss of energy for
impinging charges is investigated for this hybrid layered structure.
