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Related Experiment Video

Updated: Jul 10, 2026

Fabrication and Characterization of Thickness Mode Piezoelectric Devices for Atomization and Acoustofluidics
10:39

Fabrication and Characterization of Thickness Mode Piezoelectric Devices for Atomization and Acoustofluidics

Published on: August 5, 2020

Matrix algorithms for modeling acoustic waves in piezoelectric multilayers.

Eng Leong Tan1

  • 1School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore 639798. eeltan@ntu.edu.sg

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
|November 21, 2007
PubMed
Summary
This summary is machine-generated.

New matrix algorithms model acoustic waves in piezoelectric multilayers, overcoming numerical instability. Scattering and hybrid matrix methods offer unconditional stability and efficiency for advanced material modeling.

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Last Updated: Jul 10, 2026

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Area of Science:

  • Acoustics
  • Materials Science
  • Computational Physics

Background:

  • Piezoelectric multilayers are crucial in various electronic and acoustic devices.
  • Modeling acoustic wave propagation in these structures presents numerical challenges, particularly at high frequency-thickness products.
  • Existing transfer matrix methods often suffer from numerical instability.

Purpose of the Study:

  • To present novel matrix algorithms for accurately modeling acoustic waves in piezoelectric multilayers.
  • To address and resolve the numerical instability issues inherent in transfer matrix methods.
  • To systematically compare the efficiency and stability of different matrix algorithm variants.

Main Methods:

  • Formulation of basic matrices for algorithm building blocks.
  • Development of recursive algorithms for stack matrices, including scattering, impedance, and hybrid matrices.
  • Analysis of algorithm variants, computational efficiency, and numerical stability.

Main Results:

  • All presented algorithms effectively resolve numerical instability at high frequency-thickness products.
  • Scattering and hybrid matrix algorithms provide unconditional stability across a wide range of thicknesses.
  • Synergistic algorithms combining scattering and hybrid/impedance submatrices demonstrate superior computational efficiency.

Conclusions:

  • The developed matrix algorithms offer robust and efficient solutions for modeling acoustic waves in piezoelectric multilayers.
  • Scattering and hybrid matrix approaches are recommended for unconditional numerical stability.
  • Hybrid approaches leveraging surface matrix methods provide the highest computational efficiency.