  In this work, we investigate the dynamics and attenuation properties of a
one-dimensional inertial amplified lattice with opposite chirality. The unit
cell of the structure consists of a hollow-square plate connected to a ring
through arch-like ligaments. The peculiar geometry and orientation of the links
allow for coupling the axial and the torsional motion of the lattice, thus
amplifying the inertia of the system. We develop both simplified analytical and
numerical models of the building block to derive the complex dispersion
relation of the infinite lattice. The structure supports a frequency-tailorable
attenuation zone, whose lower bound is controlled by the second coupled
axial-torsional mode. Laboratory measurements of the transmission spectrum on a
3D printed sample match very well with the analytical and numerical
predictions, confirming the wide-band filtering properties of this lattice. We
complete our investigation by developing and solving a constrained optimization
model to obtain the optimized geometric parameters of the unit cell that
minimize the bandgap opening frequency and, at the same time, fulfill
structural requirements. In particular, the internal stresses induced by the
self-weight of the structure are kept to a low by virtue of the employed
design, with the aim to prevent plastic deformations and failure. The inertial
amplification mechanism, proposed and investigated in this work, offers an
efficient variant for the efficient design of materials and structures for
vibration mitigation and shock protection.
