A Study Of Wave Propagation In Viscoelastic Phononic Crystals And Topological Interlocking Structures

Phononic crystals or special structures designed artificially have important applications in dynamic loading protection.This paper mainly studies stress wave propagation in one-dimensional viscoelastic phononic crystals and a new kind of topological interlocking structures.In these structures,dynamic loading protection is achieved via band gap,viscous dissipation and periodic modulation,and by limiting the range of wave propagation,respectively.The phononic crystals studied include the Bragg scattering model and the local resonance model.Unlike the existing literature which usually only applies a very simplified viscoelastic constitutive model(such as the Kelvin-Voigt model),this paper deduces the dispersion and dissipation relations of one-dimensional phononic crystals based on the generalized Maxwell viscoelastic constitutive model which describes material properties more realistically and much better.The results show that for the time-harmonic propagation problem(complex wavenumber,real frequency),there is no band gap in the dispersion relation,so the attenuation of wave relies on viscous dissipation and periodic modulation;on the contrary,for the free wave propagation problem(complex frequency,real wavenumber),there is a band gap in the dispersion relation,but beyond the band gap,the attenuation of wave is still dependent on viscous dissipation and periodic modulation.Topological interlocking structures have been extensively studied because of their enhanced fracture toughness.This paper focuses on the dynamic behavior of the structure without damage,in particular,the regulation of stress wave propagation paths and range.A preliminary finite element simulation study of low-speed impact is carried out.It is found that topological interlocking structures can effectively control the propagation path of stress wave under normal impact,and can effectively limit the propagation range of stress wave under lateral impact.Moreover,this stress wave management capability is largely independent of frequency,which is an advantage that other metamaterials do not have especially under impact conditions.