Control of Bleustein-Gulyaev (BG) waves by a locally resonant meta-surface

A locally resonant meta-surface can manipulate surface wave propagation. In this paper, we investigate the propagation of Bleustein-Gulyaev (BG) waves in a piezoelectric (PE) half space coupled to a locally resonant meta-surface. The meta-surface consists of an array of sub-wavelength spring-mass resonators attached to the free surface of a PE half-space. Using the effective medium approximation, we analytically obtain an explicit dispersion equation of BG wave on the meta-surface. A finite element model (FEM) is proposed to validate the analytical method. The propagating BG wave hybridizing with the surface resonance excites a guided mode and the electromechanical coupling properties of BG wave result in a higher mode, which are below and above the resonance frequency, respectively. An avoided crossing band gap occurs due to the local resonance. Within the band gap, BG wave transforms into shear bulk wave. The band gap and wave mode shapes are tunable non-destructively via the interaction parameters. By enhancing this interaction, the band gap becomes wider while the displacements, electric potentials and stresses at lower frequencies decay more slowly than those at higher frequencies. In addition, a stronger electric field is excited by the local resonance coupled with the PE half-space. The present work proposes a simply way to manipulate surface acoustic wave (SAW) without any change on geometrical or material properties of original host substrate. Hence, this way is low-cost and convenient. Besides, the model of spring-mass resonators is instructive for a better understanding the general behavior of wave-guiding by local resonance. It is expected that the current model will be applied in practice to design SH wave-based SAW filters and resonators.