A new Stroh formalism for gradient electro-mechanics with applications to Lamb waves in piezoelectric and flexoelectric coupled plates

Feng Zhu, Nian Li, Ernian Pan*, Yilin Qu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper, a new Stroh formalism for gradient electro-mechanics is derived for the first time, which is both mathematically concise and numerically powerful, applicable to generally coupled anisotropic material systems. Based on this new formalism, the complicated Lamb wave in flexoelectric and piezoelectric plates is investigated. The dispersion equation is obtained by solving the eigenvalue problem along with the unconditionally stable dual-variable and position method. From the obtained dispersion equation, the dispersion curves and mode shapes of the Lamb wave are calculated by the 1D form of the multidimensional moduli ratio convergence method. Two important and interesting features are observed from our analysis: One is the difference in the mode shape symmetry between the piezoelectric and flexoelectric cases, and the other is the size-dependent property of the flexoelectric effect as observed by nondimensionalization. These features are further illustrated by comparing the dispersion curves and wave-mode shapes among the three different material models (purely piezoelectric, purely flexoelectric, and flexoelectric and piezoelectric coupled). The newly derived Stroh formalism offers a robust, concise, and unified approach for dealing with strain gradient electro-mechanic materials with crystal systems of general anisotropy. The present work also explains the physical mechanism of symmetry breaking observed, as induced by flexoelectric coupling in piezoelectric materials.

Original languageEnglish
Article number114103
JournalJournal of Applied Physics
Volume135
Issue number11
DOIs
StatePublished - 21 Mar 2024

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