3D complex dispersion curves and attenuation characteristics based on Drude-Lorentz oscillators for Lamb wave in various metal-piezoelectric composites

Given that many micro-nano piezoelectric acoustic devices operate at very high frequencies, the dissipation caused by metal electrodes significantly affects their performance (e.g., quality factor), but these dissipation characteristics cannot be explained by conductivity at high frequencies. This study uses the Drude-Lorentz oscillator model, incorporating the frequency-dependent dielectric properties of metals, which in physics refer to electron oscillations at high frequencies, to investigate the three-dimensional (3D) complex dispersion curves and attenuation characteristics of Lamb waves in metal-piezoelectric composites. Five commonly used electrode metals (Pt, Al, Ag, Au, Cu) are analyzed to reveal the widespread attenuation characteristics. The Multidimensional Moduli Ratio Convergence Method (MMRCM) is employed, which utilizes the convergence and divergence of the moduli ratio to accurately locate zeros of complex dispersion equations. Meanwhile, multidimensional scanning is adopted to ensure comprehensive identification of minima moduli points. Two primary attenuation characteristics are identified: (1) attenuation trends related to the real part of the wavenumber for different branches, and (2) significant jumps in attenuation due to mode shape conversions in metals with veering regions. Furthermore, a size-dependent attenuation characteristic is observed, showing a quadratic increase in attenuation as the composite structure’s total thickness decreases. These findings provide crucial insights for optimizing the design and performance of micro-nano devices where precise control over wave attenuation and dispersion is essential.