Manipulation of hybrid love wave interaction with laminated metabarrier: Dynamic homogenization approach

Abstract

Metabarriers, a periodic topological arrangement of resonators embedded into a host substrate, are the state-of-the-art structural designs that are capable of controlling a propagating wave under sub-wavelength regime. Due to their enormous application in seismic wave manipulation and broadband ultrasonic devices, a metabarrier structure is studied in the present work which consists of a periodic multilayered identical laminates embedded into an elastic half-space. Unlike metasurfaces, efficient metabarrier designs are hugely under-explored and still at infant level. Love wave, a horizontally polarized surface wave that can propagate in a layer-substrate configuration, is chosen as the studied wave. A non-classical dynamic asymptotic homogenization is adapted which provided a dispersive effective multilayer by substituting the laminated multilayered metabarrier. On solving the novel Love wave multilayered modeling problem, closed-form expression of dispersion equation, displacement fields and total time-averaged kinetic energy are derived. The control parameters, i.e. volume-fractions, heights of the laminates and unit cell size ratio, provides tunability due to which a cut-off frequency and a hybrid dispersion region are obtained within first Brillouin zone numerically for single-layered metabarrier, whereas, for a bilayered metabarrier, two cut-off frequencies and hybrid dispersion regions within respective first Brillouin zones are obtained having a band-gap at the middle. The analytical results are validated using finite element analysis of the corresponding discrete unit cell model at low-frequency. For a small-scale metabarrier configuration, band-gaps have been reported which are accurately predicted by the homogenized model and on using finite element simulation, Love wave propagation mode for pass-band frequency and wave attenuation for band-gap frequency are obtained. The present comprehensive analysis provides an insight into the hybridization of Love wave using tunable laminated metabarriers which can be utilized to achieve an efficient energy harvesting device.