Multiscale modeling and design of lattice truss core sandwich metastructures for broadband low-frequency vibration reduction

Lattice truss core sandwich structures are advanced lightweight structures that have broad application prospects in many fields, but the attenuation of low-frequency vibrations in these structures is still challenging. To achieve broadband low-frequency vibration reduction in lattice truss core sandwich structures, we propose a design of multiscale lattice truss core sandwich metastructures which exhibit a coupling effect of local resonance and Bragg scattering mechanisms. For ease of analysis and design of such multiscale metastructures, we develop an efficient semi-analytical multiscale modeling method based on a combination of the dynamic homogenization method and the spectral element method. The multiscale modeling method is verified by comparing it with the conventional finite element method, and it is further employed to design multiscale metastructures. Numerical and experimental results demonstrate that the low-frequency bandgap and vibration reduction band can be greatly broadened via an appropriate multiscale design. Specifically, a typical multiscale finite metastructure, fabricated by embedding only three identical local resonators, achieves a significant vibration reduction within the super-wide low-frequency range of 295-905.4 Hz. The normalized vibration reduction bandwidth is as large as 1.02, which is much broader than that of a conventional equi-scale metastructure designed with the same added resonator mass ratio.