  We report about the effect of an applied external mechanical load on a
periodic structure exhibiting band gaps induced by inertial amplification
mechanism. If compared to the cases of Bragg scattering and ordinary local
resonant metamaterials, we observe here a more remarkable curve shift,
modulated through large but fully reversible compression(stretch) of the unit
cell, eventually triggering significant (up to two times)
enlargement(reduction) of the width of a specific band gap. An important
up(down)-shift of some dispersion branches over specific wavenumber values is
also observed, showing that this selective variation may lead to negative group
velocities over larger(smaller) wavenumber ranges. The possibility for a
non-monotone trend of the lower limit of the first BG under the same type of
external applied prestrain is found and explained through an analytical model,
which unequivocally proves that this behavior derives from the different unit
cell effective mass and stiffness variations as the prestrain level increases.
The effect of the prestress on the dispersion diagram is investigated through
the development of a 2-step calculation method: first, an Updated Lagrangian
scheme, including a static geometrically nonlinear analysis of a representative
unit cell undergoing the action of an applied external load is derived, and
then the Floquet-Bloch decomposition is applied to the linearized equations of
the acousto-elasticity for the unit cell in the deformed configuration. The
results presented herein provide insights in the behavior of band gaps induced
by inertial amplification and suggest new opportunities for real-time tunable
wave manipulation.
