Gap evolution of Lamb wave propagation in magneto-elastic phononic plates with pillars and holes by modulating magnetic field and stress loadings

Abstract

Considering the nonlinear coupling behavior of magnetostrictive material, the modulation of Lamb wave bandgaps in magneto-elastic phononic plates composed of Terfenol-D pillars on a silicon matrix is investigated by the finite element method. By the introduction of holes, two schemes, i.e., the pillars only case for scheme-I and the trampoline (pillars and holes) case for scheme-II, are considered for exploring the effect of magnetostriction and trampoline on band structures. Numerical results show that the edges of bandgaps shift toward higher frequencies and the relative bandwidth enlarges as the magnetic field increases. The greater the compressive pre-stress applied, the greater the magnetic field at the open or closed points of the bandgap required. Compared to scheme-I, we find that the existence of holes for scheme-II can cause the closing of the higher branches’ bandgaps and the generation of a new bandgap, and larger relative bandwidth of the bandgap and wider range of the required magnetic field can be observed due to the trampoline effect. Meanwhile, the height of the pillar is a key parameter for generating or vanishing bandgaps. According to the displacement distribution of eigenmodes, it can be seen that the opening or closing of the bandgap is controlled by the coupling between Lamb modes of the plate and resonant modes of the pillars, which is induced by the combined effect of trampoline, magnetic field, and pre-stress as well as geometry parameters. These results give guidance for active controllability of Lamb wave propagation and intelligent regulation of phononic devices in complex environments.