Piezoacoustic wave spectra using improved surface impedance matrix: Application to high impedance-contrast layered plates

TL;DR

This paper develops a matrix formalism to accurately compute piezoacoustic wave spectra in layered plates with high impedance contrast, enabling detailed analysis of guided modes and wave phenomena at high frequencies.

Contribution

It introduces a unified surface impedance matrix approach for piezoelectric layers, extending to multilayered structures and providing full spectral analysis at high frequencies.

Findings

Successfully determines spectra of guided modes in multilayered plates.

Reveals wave confinement and asymptotic behaviors in high-frequency regimes.

Analyzes negative slope and interfacial wave phenomena in layered structures.

Abstract

Starting from the general modal solutions for a homogeneous layer of arbitrary material and crystalline symmetry, a matrix formalism is developed to establish the semi analytical expressions of the surface impedance matrices (SIM) for a single piezo-electric layer. By applying the electrical boundary conditions, the layer impedance matrix is reduced to a unified elastic form whether the material is piezoelectric or not. The characteristic equation for the dispersion curves is derived in both forms of a 3-dimentional acoustic SIM and of an electrical scalar function. The same approach is extended to multilayered structures such as a piezoelectric layer sandwiched in between two metallic electrodes, a Bragg coupler, and a semi-infinite substrate as well. The effectiveness of the approach is numerically demonstrated by its ability to determine the full spectra of guided modes, even at extremely high frequencies, in layered plates comprising of up to four layers and three materials. Negative slope in f-k curve for some modes, asymptotic behavior at short wavelength regime, as well as wave confinement phenomena made evident by the numerical results are analyzed and interpreted in terms of the surface acoustic waves and of the interfacial waves in connection with the bulk waves in massive materials.