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            <funder>FF acknowledges financial support from the Italian Ministry of Education, University and Research (MIUR) under the P.R.I.N. 2017 National Grant‘ Multiscale Innovative Materials and Structures’ (Project Code 2017J4EAYB.</funder>
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                <term xml:lang="en">Prestress / Prestrain</term>
                <term xml:lang="en">Band Diagram Tunability</term>
                <term xml:lang="en">Inertial Amplification Mechanism</term>
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              <p>In this paper, we report about the effect of the application of a state of prestress on the band structure of a periodic phononic crystal characterized by an inertial amplification mechanism. Through a numerical example, we show the possibility of inducing negative group velocity in an isolated branch of the dispersion diagram. A 2-step Updated Lagrangian scheme is adopted to calculate the dispersion diagram of the structure. The proposed method include (i) the static geometrically nonlinear analysis of a representative unit cell undergoing the action of an applied external load and (ii) the BlochFloquet decomposition applied to the linearized equations of the acousto-elasticity for the unit cell in the deformed configuration. The dispersion analysis is performed in terms of small amplitude motions superimposed on a deformed state, once the desired load has been applied.</p>
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