Design of vibrational filters based on 3D lattice material elongated structure

This study examines the potential of elongated periodic three-dimensional lattice structures for the design of vibration filters using so-called absolute band gaps. These filters are generally obtained by modifying the total stiffness of the structure, which decreases the propagation velocity of all wave polarisations. With a view to optimisation, we are implementing an original structure consisting of interconnected 3D beams with a sinusoidal accordion shape to control the speed of longitudinal waves. In addition, a central junction in the shape of a deformed cross controls the speed of transverse waves. To calculate the propagation of elastic waves in such structures, we use spectral element methods that take into account the longitudinal, torsional and bending motions of three-dimensional beams. The dispersion curves are obtained by applying the Floquet-Bloch periodicity conditions. They are analysed by a detailed study of the wave motion and polarisation. Finally, the geometrical parameters of the lattice cell are optimised using a genetic algorithm to generate the widest absolute band gap at the lowest frequency.