Wave propagation study in metamaterial sandwich structure with periodically inserted hourglass resonators

Low-frequency bandgaps are generally achieved by using locally resonant metamaterials at much higher wavelengths than the lattice constant. However, it remains a challenge to control wave propagation and vibration in these structures due to the limited number of conventional options available as periodic unit cell arrangements. This work investigates the band structure of flexural waves in a metamaterial sandwich beam with an hourglass lattice core using the transfer matrix method. The double dome-shaped hourglass unit cell is modelled with different non-dimensional geometric ratios. A sandwiched metamaterial beam model is then established using a periodic finite hourglass array, considered under the flexural wave propagation. The complete hourglass sandwiched system is further studied to obtain the bandgaps corresponding to the microstructure of the hourglass which is varied in the frequency domain. Subsequently, parametric analysis is performed using some specific non-dimensional geometric parameters that are found to be sensitive towards tailoring the mechanical properties of such unit cells. This study builds a foundation for modelling lightweight hourglass lattice sandwich beams with complex dome shape structures and presents guidelines for designing sandwich beams to control wave propagation.