Evanescent Lamb waves in viscoelastic phononic metastrip

In this paper, the propagation of evanescent Lamb waves in the one-dimensional viscoelastic phononic metastrip is studied. Complex band structures and transmission spectra are calculated by using the finite element method. The effect of viscosity is included according to the Kelvin-Voigt model. Two types (namely H-type and I-type) of metastrips are fabricated in either steel or epoxy. A theoretical model is developed to predict the distribution of the displacements of evanescent waves in the finite metastrip. The effect of different cutting forms on the complex band structure is also investigated. It is found that the spatial attenuation of evanescent waves is clearly observed in both simulation and measurement. Numerical and experimental results agree well for steel metastrips when only the elastic stiffness matrix is considered, whereas good agreement for epoxy metastrips is achieved when viscoelasticity is taken into account. The displacement distribution of evanescent waves can be accurately predicted from the two least evanescent waves identified in the complex band structure. Different slicing forms for the metastrip result in the reconstruction of evanescent waves, leading to the opening or closing of bandgaps. The present work lays the numerical and experimental foundation for practical application of phononic metastrips.