Dynamics of elastic lattices with sliding constraints

This study investigates the impact of sliders –constraints acting on elastic rods allowing for atransverse displacement jump while maintaining axialand rotational displacement continuity – on thedynamics of a periodic elastic grid, including theeffects of axial preload. The grid is linearly elasticand subject to in-plane incremental deformation,involving normal and shear forces and bendingmoment. The periodicity of the infinite grid permits aFloquet–Bloch wave analysis and a rigorous dynamichomogenization, leading to an equivalent prestressedelastic solid. The investigation is complemented byad hoc developed F.E. simulations and perturbationswith a pulsating Green’s function. Results showthat the sliders create band gaps, flat bands andDirac cones in the dispersion diagrams and generatemacro-instability even for tensile prestress. The lattercorresponds to the loss of ellipticity at the parabolicboundary in the equivalent elastic solid and providesa rare example of an almost unexplored form ofmaterial instability. Therefore, our results offer designstrategies for metamaterials and architected materialsshowing reversible material instabilities and filteringproperties for mechanical signals.